Question
In the adjacent figure 'P' is any interior point of the equilateral triangle ABC of side length 2 unit –
![](data:image/png;base64,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)
If xa, xb and xc represent the distance of P from the sides BC, CA and AB respectively then xa + xb + xc is equal to -
- 6
Hint:
find the areas of smaller triangles and sum them to find the final area which is equal to the area of the larger triangle.
The correct answer is: ![square root of 3](data:image/png;base64,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)
√3
AB=BC=BC=2
Area of triangle ABP = (½)(AB)(xc)=xc
Area of triangle APC = (½)(AC)(xb)=xb
Area of triangle BPC = (½)(BC)(xa)=xa
Area of ABC = √3a2/4
= √3= sum of areas of smaller triangles = √3= xa+xb+xc
area of equilateral triangle = √3a2/4
area of triangle = 1/2 x base x height
Related Questions to study
The expression
is equal to -
In a triangle ABC, cos A = (b2+c2-a2)/2bc
The expression
is equal to -
In a triangle ABC, cos A = (b2+c2-a2)/2bc
In the figure, if AB = AC,
and AE = AD, then x is equal to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASgAAADICAYAAABbNHwvAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AADEHSURBVHhe7Z0JuI1l98b1T+X7hKJ8hkyZQiiRolBkKJEppAiFZEhSSIZEZciQIUPmUJlShmQqn8wkEX3mMfN0TIn7f35Pe5uHc5yzz3n33ut3Xe9V9nsO5+z9vvf7PGvda60EMgzD8CgmUIZheBYTKMMwPIsJlGEYnsUEyjAMz2ICZRiGZzGBMgzDs5hAGYbhWUygjDjgrBSxSSvmzNQ3s1Zr+ynpjO+MYVwLEygjDjir00vfV92HsilZvmbqt/aMTkZqlmFcDxMoIw44pd/7PqPSyRMoQfqnVGP0du2PXEUZxvUwgTICzGmdPfOrRpSvr+dTJVaGJ7Lp/kbfacXB077zhnF1TKCMwHJit/Ytaq+Gtfrr46YN1bJWbt1RsJUGrzmiE74vMYyrYQJlBJTTu3/VwlalVLf3ZM3+Y5V+altW2e8qple+3qxtf/u+yDCuggmUETjOnNDulRPUtsrL+virpdoSud3b8PUbqpUqpR5+ZYJ+2PYX+T3DuComUEbgOLBEv4xppofe+krjfzvmXjq1drT6PpNUqVPWUOtpm7TfvWoYV8YEyggYR1d+oYnvPqQaI9Zp+VHfiydWaknnQkqVNLWKdZpz/nXDuAImUEaA2KPfI1dP1dMlUOaCpVWiwvOqUqWKqlQqqVJ5UijBTTcpSfVBGrX2pO/rDeNyTKCMwHB4qqZ0r6QH8lZU+YqVVaViBVWoEHlE/n+l555WsXsTKmGWOnpr/FaZJcq4GiZQRgCI0J5JH6rL283Uct4xRVwaCT+1Qyt7F9GjyXKpePPvtMKyecZVMIEyYpmzOrJ1nD4sW02lCrfX6B1HdPRSgTqzR7tmt1GNTLcrRe7aajF5u/YeOq4zZyynZ1yMCZQRq5w587d6vlZNaRPerlsTptdDz7bUgOUHdMB3XtqtXfN7qunj9ynlLQmUIMG/lSxzeVVpM037jvzl+xrD+AcTKCNWOXv2rOaOn6z+/fqoX//e6tv/G83fdkzHfeelIzq84UeN79dPfT8bpIGf9VHvnp9ryJQ1ijhpez3jYkygDMPwLCZQRpywfv16/fbbb4qIiPC9YhjXxwTKCDh//vmn6tevr1KlSmn06NH66y+LNRlRwwTKCCj79+9XixYtdOedd+r//u//9PDDD+vrr7/W6dPWbsW4PiZQRsA4cuSIBg4cqNSpUytBggS69dZb3VGoUCHNmDFDZ85Y41/j2phAGQGBbdy4ceOUO3duJ04JEyZUtWrVVKtWLd10000qVqyYZs6c6bJ+hnE1TKCMgDB79myVKFHCiRNbu3vuuUfjx4/XunXr9OyzzzqRIiY1d+5c/f232QuMK2MCZcQ6v/76q6u7u/3225UhQwbddtttevLJJ7VgwQJ3fuXKlXr66ad1yy23uP/6XzeMSzGBMmIVMnZ16tRxolSwYEHVrl1bd911lxo2bKht27b5vkpavHixihQp4kSKLgeImmFcigmUEWscOHBAzZs3d+L02GOPqXfv3qpataqSJ0+uwYMHX2YvYHuHSLENJD5lImVcigmUESscOnRIH3/8sROne++9V1OnTnVxqKxZsypTpkz66aeffF95MXwNWT1Eqnr16i5GZRh+TKCMGIM7fNCgQc5OkDJlSvXp08dl50aOHKmkSZOqbNmy+v33331ffTmzZs3SQw895EQKQ+emTZt8Z4xwxwTKiBEYLsnO5cqVy5kx27Ztqz179ujYsWNq2rSp7rjjDrVv31779u3zfcfl4If65ptv3N9x8803q1GjRtq6davvrBHOmEAZMYKtW/HixZUoUSIXEPcLy6JFi9zWDXvB999/f11T5qlTpzRp0iTlzJlTiRMnVuPGjbV7927fWSNcMYEybhjiRQTB2ZphF1i1apXvjDR06FClSJHClbZEdctGEP2rr75StmzZ9O9//1utWrW65srLCH1MoIwbAsvAa6+95sSpQIECmj9/vu/MP7Ru3dpZCLAckN2LKmwZhw0bpixZsuhf//qX+3uwLhjhiQmUEW1Y1bz77rtOgFjtfPvtt74z/7Bz505n1MT/9Nlnn+n48fPt6qIC8SuC7mT/WEkhUnv37vWdNcIJEygjWiA2PXv2VLJkyZQmTRp98cUXvjPnQbCyZ8+uBx98UMuXL7+herujR48671S6dOlcgfEHH3zgio+N8MIEyogWI0aMcIFvVkcI1eHDh31nztO5c2fnh6LmLiYN6mjV0qVLF919991OELt27eqC6Ub4YAJlRBlWRmTZ/AHsK2XZiCFhuMQuwNfEFCwLGEAJuP/nP/9Rt27dor1lNIIXEygjSvz888+uRQpdCF5++eUrZubYyq1du9YFzTNmzOjarcQGxJ86derkRAoj6IABA3TypE0kDgdMoIzrsnr1ahf0pm0KrvAlS5b4zlwMojF8+HClSpVKZcqU0f/+9z/fmZhDJu+9995zWz1KaYYMGeLiVEZoYwJlXBNWSq+//rrb1lGOMm3aNN+Zy8FOgHuc+FOTJk1iPV60ceNGNWvWzLnTESm8VrbdC21MoIyrguAQ8KavE4LAlu1aAw+2bNmiokWLulVO//79fa/GLojUG2+84f4NLA4MYbCunKGLCZRxRRCifv36ue0aGTt6i19vtfLf//7XxZ5Yac2ZM8f3auyzYcMGV1aDDytfvnyaOHGi74wRaphAGVeEySuZM2d2dXEEqK8X7+F8r169XO8nguiBLvZlxl6NGjVctpByGur4rHVw6GECZVwG7U9YmRBLogEdqf7rQUCcpnMIWo8ePeIky7ZixQo9//zzbiADIsUQBpsUE1qYQBkXwU1PHAn3ds2aNd12KipQi0e7FNzljJSKK5YtW6Zy5cq5ur3SpUu77go2cy90MIEyzoGHiRUJ4oQLnJYpUWXUqFGuHxQiwfYrriBAjkeLCTKs+OiqcLXunUbwYQJlOMjAvfnmmy5jlz9/fmcniGpMByMl04PJrL3zzjtx3n2AbR0rOPpSEZPCs3U1r5YRXJhAGU5gOnbs6ASGLNyYMWN04sQJ39nrs3TpUj3xxBMu2zdhwoR4q5dDpJgk4+9vjsHUCG5MoMIcxITSEWJHlJKQiYuOOMGXX37p+pE/8MAD+uOPP3yvxg9TpkxxPweud6YY26SY4MYEKoxhazR58mQ3npytHaUk0XVm83e8//77ruUvQfWoZPwCjV+k8Enhl7rWwAbD25hAhTFsiR555BEXFKc75q5du3xnog7N6bAXUH5Cp4GYtFeJLYidMfYqb968LrtHbM2GMAQnJlBhCpm2UqVKuXjNCy+8cMOFvXim8uTJ49qwzJs3zzM+JKwG9DendTCxNfxcF042NoIDE6gwZP369W47hjiRnmcM+Y1C0zpWT9gSGN7pJTCL0vGT4aEYSMkwWuvg4MIEKszYvn27K7ZlW0dLXkZC3WixLfV6DEUg1vPWW2/5XvUW/G6IFMXOxMmIl0VniIMRv5hAhRG056W3N9k6tmRM/r3RdiXc+LjMmX1Hp0v6QHkZ+puTaUySJIk++ugjG2cVJJhAhQlsd7hJKQCmK2VMW+diT6CgGN8UHiivp/OZFNO3b99z/c1pI3ylfuqGtzCBCgMIGE+fPt21QSHuhJmRgHZMIN7UsmVL18iuQYMGQTHMAEH69NNPnUhx0E7G6va8jQlUGEBN3VNPPeXKQDAwsuohuB2TjBsDE/g7iet88sknvle9D8JK+xh8XxkyZHBz+4JBXMMVE6gQB5NixYoV3cqpUqVKql+/vhsbRTsVGszdCMSfqHUj8Hzfffc5z1EwQa1g+/btXe+qtGnTumZ81+oUasQfJlAhDBm7evXqOXEqUqSIG6KJYdGfeatcubJ7LboQz6KlL8F2msbRhjfYwPHerl0714EBkaJ1cHRLfIzAYwIVohBvocMAQkTZx4U9mrAW4LImfoRJk2Lf6MRiyN7ho2KbRLA5WOM4O3bscN4o3OYkD6gptO2etzCBCkEo9ejevbszUGbKlMn1arrwxmOlwBBO2qpwczIiipq8qHTBRPjIhvmnC3/zzTe+M8EJYtu4cWMXS8N1TicHwzuYQIUYCBH+JuJDbF9Y4VypnzgiRs+nJ5980rXMzZ49u1sVETRGvFauXOlq89atW+e+jpHnb7/9tnOM48xmgCfZwOg0tfMqlPkgUqw2KZy+1mgtI24xgQoh2Gpxc7GlY2WEu5s41LXAboCzHFc530PgGLGiBIYi4Geeeca18iUtT8dKjI4clI7wfaFShMtKitgcYk0BdVy2LTaujglUCEHrW1L/lLG89NJLUW4zgolx9uzZatWqlRMmBI6Zc8RlECv+/Pjjj7tpLcS1yADiHqcYN5RiNr/88ouLybGSQqSI1dmkmPjFBCpEoFFczZq1lPCW2/RMuXL6fe1a35moc/b0Xzpy5IhWrVrlBGvGzNmav2ChW12cPn1SZ/4+rfHjxilDxozOXsDXhRrYJ6pUqeJiUo8++qjmzp3rmQ4N4YgJVAhAyrxx4yZu21Ww4MNaMH9+1J/8VykUPhP58lluzDMX/z3du3dzNy/DFW6kf5TXQYyIq5UvX979niQQFixY4DtrxDUmUEEO9XTOGZ04qQoUyaEvBzXT4GoVVbl0aZUoXVZ1OgzS9J2+L76Qv/fpz+/bqGHVkpHbupJ6+f3hmn5JJ5LDK77U5/XKqHTk31O6bG/1/26VqjVtoDuSJXXBd1ZboQrN/KgxJCZFYoA/G3GPCVQQQ/ynX9/+uvvulMqcM7naN3hJI15vo3b1X1eDunVVt2RW5b7vUZVsu0irTpzWuY3K2T+1fcZANXricRWuUFl16lbT82XL6JUmgzV3q+TMBltnakKvhqpRpY5eql5Vpe7Npceeb6D0+R5Xzvuyac6c2SFfx8YgUGYEkrHEhR+KW1qvYwIVpCBOBKnTp8+oO+9Mrk97NtXMngPUte4YLfZXbWz/Sj2fe1y50jdR//8dkd9scHzDaI19rbjuK9JPIzYgR39r/bD6avxgQVXov1mrI/7Wscm11aLFK2o8132Hdn1dTkULZ1OCBHeqTKmSkdvK3ZwIeQiUE4si8cAQhjVr1vjOGHGBCVQQQnyJNDjZtMS33643mzfX9uXLdGL/AW09dUbn1zXrNad7M72Yo4EGLj2s/e61CK0c1kBvPVVAb4zfq83+L977vb79oJaylO+vUav2a/3YKqr3UhnVmujL0u0aoudL5IoUqNucvSCcsluM0sJqgXP+lVdesSEMcYgJVBBCELds2bLOt1S1atV/5r/9dQXBODlfXw/vpVffmapNe//+R7hOL9a4NyurZK4X1GP5cZ1v0rtGSwY2UrHML6jNxPVaM6u9GlUuoQJvz9Hag/u0Y2YHlciZTKnuyaghQ4f6vic8wGHPahWRwgPWsGFDZ2A1Ao8JVJDBjYEfieAtk3Spo7tiy96/l2vioH5q22OGFkSK0zn+HKsez5dT5tzt9cX2YzpfHrtbv09oodqpcqpOz2X69cBGzfmkpkpmz6b8jxVR0bxFlDzRbSr+1JNaumyZ73vCB8qD/CJFthQTLLV8RmAxgQoi9u/f78pNECcmqRDEvYwTe7RjTi992LiQMqXJoywF3tSnY1fqnN9741B1Kl9OqfN31YSDxy/YDh7R+plt1CRNGtXotFBLIjXv782zNfXjpqpft54yZi4eub1LqPr164Z09u5asK2l60H69OndSurdd9+9rlPfiBkmUEEC9XQ0hqPFCY3WrlrUGrFdG8a9pbqVn9JTD6VTmltvVsK0r6rzigM6jBptHa7OfoE6cKFA7daaCU30YurUer7TAi24QIOOnziuypUrRm4pEzl7QThD5pJJzIgUKymGndqkmMBhAhUEkLEbNmyYa/pPBwEKeq8+ieWszv592jVgO7n8c3383B1KfHd2Pd5ludbRgnv/GHWpVE4ZHuikL3cf1/lClQ1aMbimnvpPBlXpuljLjvlejoR+47ly5XTlLxQShzuYOREpyn0oyO7Ro4db3RqxjwlUEEArFOriKNZlbFLU589FaPWIuqpTOKOKf7xYvzBt6cxPGvlaRRXOUU99VkZcFCRf/Fl9lUhbUm+MWq31PtMURlDEkZuxQoUKlsHyQf1inz593ACGVKlSuRbKXpsLGAqYQHkc4kzYCegn3rRp02jHPA7+9LEGvppFdUdu1Gq3bdunBb1rqcFjhfXeD0e10+/e3DVVX7UppyyPttFni/48FzxnGi9tgin76NChg3WdvAB6YzHCCpFKkyaNG8iAcBmxhwmUh1m2bJlKlizpWvZiJ4j+ePJdWj6qnRq/VE8jfj2sA76A08GlvTSgQVE9/PZ8LfLdT/vGNVXjB7Lr0fcWaNH+8xs/+kI9/PDDLvbFmCnjYg4ePOhEijY1xKUY7RXqDvu4xATKo2zevNm1TGEKCyK1cOFC35mrELFZ6+ZPcLGRc8egD9W6XW+1671E205ccNMcX6tVEz9Wucr11OD97pFf+5FavlRKL5V/RyN/Oa1DF4S3pkyZ4mJfuKlDoTldICCr2bFjRyVNmtRtxelgaivN2MEEyoMwdQQ7ARc8jeQmTZrkO3MN/pyliR9UcW1Qzh0F66nR5ysiN3VX4MgGrRr8kso8+s/XPvlqJw1bQ9HLediuUIjMz8Hsu1BpThcI6Cjh/8xos0yW1SbFxBwTKI9BoLV3794uKE3fb0aKR6kp3OkIHd6zxfWFOnds2KXdR6623YhcJkXs0raN/3zt5t2HFOE74+e3337Tc88957Z3bF2i9HOEMbSfYQgDdXuIPsmNq2dbjahgAuUhSF/z5GWwJnVfXbt2jVdTJPPu6KjJMAEauRnXh1UmyQySGphpv/vuO98Z40YwgfIQCALjoGg5y1jx+DYAkpViNBV9yc0xHXWYE0hRMckNMrDBNtjUS5hAeQSC4IULF3a9h4j3xHe3SlLor776qitIZsAl2Soj6rBtRqR42BQoUMC1DjaijwmUB6AAmO4EbAvoh83FHd/Q5rZQoUJufBXbFAv4Rh9sIRR2Y7Cl8R2j5q2/efQwgYpntmzZcu5Jy4w6LmIvgHschzQj0217d+MwKYb+7QTOmYxjrYOjhwlUPLJ7925XEc8EYEY7YSfwismPpnSs6OrVq2fZuxhAFg//GGVCeNpKlSplCYdoYAIVT5Cdo5aLVQoO5KFDh7q6Ny+wc+dOdyNRwkGg3FLlMYeZhQxfYKVcrlw518fLuD4mUPEA8ZwvvvjCdQegRIJSCa8EoYmR0Icbe0H+/Plt5FIswvaOJoNk91hR0SUiuvw2ebKGfNJbn/YboMGf9Vav7l3VpUsX39FV3br3Ve+Jy7Vmrxt9EfSYQMUDCAD1bQRPmzdv7ql+QpRo0PMJR/SLL74Yts3pAgWWA+J6NB0kNsVQ1OgwuUULPZcltVImvU0J/p1K6bLlUu7cuX3H/cqRNadS5m6mnrM3XNAtNXgxgYpjKL71jydHALzWNpa+RmQSEU/qy4zYha6c1DeSIaXhHTE+fFNR5diBA9o982O1qZpfd5XopMHz17lryB07t2ndkun6tHobDf9+2fkuqkGMCVQcQtq5Ro0aLlhKHMKLvZWY/Xb//fcrXbp0rge3EfuQdKAzBKseVqqIVLQ6VWz6Qv0alVCGKkM14wrTvyLWb9GeA4fljYhmzDCBiiMwXmLAZGlPuvmnn37ynfEO3DiIEoF7OiiQIjcCA4XYxCGJ9WGGbdKkiTZt2uQ7ex1WDdYn9YopXYX+mrTh/Bb86O692rBiifZTZxkimEDFAfv27VP79u3dhcjqxKtFpNgeiIlRB9iqVSvnJjcCBw+EESNGKGfOnC5jSqFxlLb8qwape73iylB1pGbTJdXH7t9+1vA2n2nJ1j3/TIcOAUygAgzDDkjVp0yZ0g07wE4QEXFp3wBvQPcCVndsO3i6G4GHBxUdK+gjRX9zyopot3NNfhuq3q8WVMrCjdVu2CRNnz498himXh+01guVPtdPGw6dH3Mf5JhABRACov5l/N13360PPvhABw5c8MjzGEwrpnUtptF58+b5XjUCDbYTBi/QGJAHGatt+ktdlTWjNbBuZiVKcpdSpc/kxC1z5nRKk/ZBZSk/WLO2e/MBeCOYQAUI/ESzZ892BcDEnV577bVrX3TxDPaCXr16OVd7zZo1o53+NmIGPjhECoFKmzat+vbte/UttltBPaL/PN5MHb+Y4q6z2bNHq99HbfWSbwUVKlEoE6gAQYCZTB0ZO9L2Xh+VvX79epdhRKD69+/vGVd7OMHqmh5gfAZ05byqSF0lBrVn9UKNfG+Almw7aAJlXB18LbVq1XLiVKJECTf8wOtgHs2RI4eLk1lBa/zBSootHh4pPgt6y1/2sLhKFi9izz5tWrlI+7VD6zft1Y4twW/VNIGKZfzjyam5olkZy+9ggGGgZO8oxbDtXfyCSFFEzpBWHhojR468eCXl90E9P0wzLosaHNWhP/qo78DvNeW/R32vBS8mULEIcRxqonj6UWc3btw4Fyj3OidPnnTdC+ieibhiizDiF64lRIrPhP7mAwcNihSpIzoW+dnsnN5ZrarkU4on39dnP/7mJgBx0LpnzcKR6lY+u+q0H63vtgf/Rs8EKhYZOHCgy9Yx8ID/96qd4FKWL1+uJ554wnVVmDBhgjWn8wjTpk1zNZsUF2eNFCl6dH1Rv76qZEmjlMkS6abEqXRPlvuUK1euc8d9WTLq7ltK6I1RS7TR+8/G62ICFUtMnDjR2QnYJjGBN5jGYGMWJMXNzRCdujAj9sEDxZaOrC9FxTzsECgO+tV3b9xYX302WIOGDNeIIQPU/9PeLvvqP3p/OkADhizUyl3HLhohFqyYQMUQ7AR0wcROQAFw48gLKNg6UDKgASsEWTwb3R33sNKmrQ3ZU4a14kUjhsk0nTp16jj/XM3I13ntqWee0bKVK33fGfqYQMUQ7ATMjqP6n/YZdCsIJgi+li9f3rnHu3XrZtu7OIIHG3EjajIRoMcee8x9BgTGGbLAg47ttn8lzkOPB4i/ljNchjCYQMUAijtff/11JUqUyF1gwZae5yaZM2eOqw/EPf7jjz9a98wAwwqVYDYhgdq1a7uhFPie2MrRk55tGp456vQu/SzWrl2r6tWru+utWLFiLnYY6phA3SA82fCrEHMiOImPyCv9xKMK2btPPvnEPbkrV65so6UCCNcGq21WqXjjmBrt9zrVr1/fTc4h/kft5rVYs2aNEyk8dswrDHWRMoG6AbAO9OzZ81xZwqhRo4LCTnAp3AzEPNg2tG7d2veqEZvQLXXs2LGu1Q5bN7oWcJQuXVqdOnVyhb6sqKIDxl/6mxM4L1OmTEgPYTCBiiYsuykARpiwFFCOwEokGKFJ2kMPPeR+l9GjR/teNWIKcbzFixe7LhbEjVglkUDJmjWrXnjhBTcsY8WKFW6LfaMQVGewBSKFWK1evdp3JrQwgYoGrJJ44mGcY1vEFi9YvE6XwpYDIynixJaDG8aIGQS9Z82a5YZgEE/iGiG+5A96M1YsNrfRTIphBcV4MIQvWl05gwQTqCjitxPgTSFj16hRI23dGrxdn+msQIO0JEmSqGnTpq5Ex4g+bJO3bdumb775xg1gJeiNMOErQzwYQEFmNxAhAFbziBQBc79NJNTKlEygoggXGV0JCGxWqlQp6FccZIpo60spxeDBgy17F00QHHrKU9rEagnvEmKPQCFUrJZYUQV6Kg4PToYwYLIlu0dmEMEMFUygogBBTJboiBNPK5q5xSR+4AWwF3BT0W4We4ERNVhpjh8/3jm9EQW6YCLyrKxZLVEcjjDFJcRAWcEVLFjQiVSwr+4vxATqOhAzoHQFOwGxp2+//TboVxu07yC4z+9UrVq1kIxdxCZ4kghK854xKowOlmypWC2R8u/du7c7H5+ZXGKKTIrB04Zg8kANhbIlE6hrwJOpX79+zk7ApBO2QsFoJ7gULly2AsRK8OUEU91gXMLKmRURdgBWSLxfWARYObGCYiXFoAmvgAmUOj5Wxf6hsF76+W4EE6irwBMJt68/6EmsIdiMmFeDLR3OcQK54VIyEVUIerNFY8uEdwlrALEltsNs7z/88EM3XMKr1wKr488///xcH/z3338/qA24JlBXYebMme4mxrFLtiuUVhm07SD9TXDXtnf/gOAwtJRSExzaiDerJQp2WW3ysKIe7npOby+ASNGAkK0oJTRMiA7W69cE6gpQPsDT8qabbtLLL78cUi1I8G0huP44RbBvAWIKWTbmFLJlw7RKsS6xObZ0rJbY4lFzGWxJEQSJ/uYpUqRwqz9KmoJRpEygLoHlO3VprJwqVKgQdN0JrgeOY8osiKkRr6BzYzhCXRyObrxDJD8wO+L45s+UMRH0DtYKAT88fDp37uw+a5oRXnNSjEcxgboAlvDEHRAnnqCY4EINRpszMYTVAtXx4QRB7x9++MElBp5++mm3hSO+SO94CnapmfPyaLAbgUkxBPlZGbLlYwhDMMWkTKB8sPyldAVfS+7cuYOmn3h04XdkBHvVqlWDtkwnOrCFY4tO+1wePsSU8LNR4kMMDu8SdXOh3AcLkWKUPXFHkj5ko7FOBAMmUJFwow4aNMgt8QmOsvQPlg8wOhDgxQ2PmY/AaSj+joBPjd/tjz/+cNs1ag2Jw/jnzeFlwjNEti4cRBpYGb755pvu4cSKkbhbMIhy2AsUqyTKEohD8OFhygzFujRu2kWLFrmtHRNnpk6dGpLlLcRYWC01a9bsXNCbFRMFu6we6WDJiipULCPRgRAG03uwTeDlwkrhdZEKe4GiAPiRRx5xbSsomt2xY4fvTGjBhUjPa25YJh7TpyiUIOhNEJj+VhgVaW/Cqok/syLG+xVsAeJAQBzu1Vdfddd7/vz53UrKy6GMsBYofC9ly5Z1HxbZm1CpX7oSbGUoYiVbhcM4FOBhgl+NOBKdA1gZYBFgtcTvSt8upqQYF0NyhG0uNppChQppxowZvjPeI2wFCjHiQyJjR0YnVBt++SHewkoxefLkLt4WrPiD3mxR2caxNUeYCHrTF75t27au42QoJjhik/Xr17vVpZsU89RTbuvrxfcsLAWKrAZ7ceqVeIJgxgvldiNceNzQGTNmdDcxHp9ggs8GvxZBb5zePFAQJMSW36lWrVrOIsD2JVyC3rEBvaNoHcR9gEgR7vAaYSdQZLLoeMjFTb0SF3Yop5gB3wtZO3w/OKaDyQdDASxdKokPsnWjvoxkBq1FGNfEOVaHoZqRDDQYkRk7RpgD4ceo7CXCSqAQJwopsRPQoYA2GcFQWxVT2BJRX4a9gN85GGDLTVCfVrZ58uRxooQFhNmDWAfYkgS6GVy4wJbYH4vFhkJs1iuEjUBRS0ValQwP7mFiFeESQGVLx1aIgxS8V+HzIGBLDRmDAFjlsv3wO70Z0U5dnBH7IFL+IQyIlFdWUmEjUJSt0OKWCx5HcSi1Rb0W+H2GDh3qTIoVK1Z0bWq9BFs4OioQB+ShwWqJQmbmxhUtWlTt2rVzA1GDvS4uGOAeYWoxIkUCyQv9zcNCoBh2yNYAbwxjykOtsfy1QIhpAYtAUZPlhYp2VrO0BCF2REaRJzdbbv82jif4l19+6YyFCFgoJzC8BO8zfjESKYQDvPAgD3mBwuJfr149t3KihcrChQt9Z8ID3ONkKjFoMr02vm92smz8HC1atFDhwoVdpT03A54cntxk5NhuhKPT2wvw8ECkHn30UbeSRaTi0x8Y0gLFaoFtA+JE8zkvG9ICBVlKCqDJgMVnXIGtJU3Uatas6bxLfCY0U6OnNwMuKWZlW5c3b16XyDC7QPxC+RefBT7B+OwbFrIChTjRVoOAOG1buVHDDeI2xHAQA+wFO3fu9J2JG7ioiS1h6yDozTaTnwWxZFU7ZMiQc09nvhbbAGJKiQrZRsvSxR9Yb+joQUyQFS5NDuP6+oGQFChMfVz8XOjENnhyE/MINwg+ExjnPWBVQjwn0PBvYKhkG/f222+7Cxynd7p06dxWk9cIxl6pQyXfS5wMkSLjSEO9S7d6f0Uc1MbFP2j2D3MityILtGr9Rm3du0Wr5/6o2dN/0rIN+3TIQlaxgl+kmBTjF6m4XkmFnEBx4TMaitQ07U7DyU5wKYgEZlSsFbQxDhTEtfCTkXxACFkt8XDg/cfxjZdpzJgxLih+vQ6ePEhatmzpEhqYMZcsWXKRmB3esEKDX8yj/KmT647k96tsm74aNWuImmVMr2wZHlPtz+ZrlVW5xBo8NLB30EeL1e+7774bpw/7kBMo7PrY9gnwUTDKTRGu0O6VJx+Zy0C1kEFweM8JerN1IwvHiolWJ2wvKeZlGxcdmwBCR2zKn0kim+fn9LHD2rZ0mia3fFxZshdVsc5ztWTlzxrxQjV1GvGVZm09oCO2gopVePgMHDjQtQ1mdYtPLS5W4xBSAkUBJIMoyQhh3/ea5ycuIchMMSipe4Qitn1EVMRz0fJvPPjgg67nEhk53neC3ji9YyKKrP5y5Mjhntz8XZexd6b6NnlOxR4qp2qvtVT30Su02YQpYNCqhnY2VGGQ3GAMW1xYVkJGoNjGNWnSxGUd2BqEYj/xqMKWixorYj60eMVBHxuV6vSQ+v77790TlJ5S1MWxFSNDitN7+PDhsdYVgn+LbgUE1gmeX6l+8MiSTmqaLbn+nbyE2q2M3B76XjcCA4LUvXt3Z1khrknhdqATGSEhUFy8bGfY1tEtkiZc4QyBZWJBrGhodxuT8hC2cATbKZEhSMqqhlgEMSYGS7C1mzNnTkCKdZncy++AkfPyGNoJ7d40S0NqV9AzeSuq0dC1Wn/SllCBZteuXW4YKFt5EhmsogMpUkEvUGQaWHoSkCVTNGrUqCtmiMIJ4gPYCmhO9/rrr0fbnMn7x0VHLIgAKZlABInaON5jVk8M/6RhHFvHQJk/V6xY4bw4bCEv9rCd0emjP2tU9zHq17iFPmn8tPI82FgfzNusA76vMAIHmTxEiq0eW3Ay5oEqRQp6gaL5PftigncsOcOhO8H1wK9CHRvbIzoCRAdWTKyIsAOwReRJSRwLkcBMydgmEg9xkckhzoX7n1XxhAkTfK9KJw+t1ZRW76tPv++0bMsO7V40TJ0qZlT2hn00cmXcBG/DHUSKbCv3HVliLCGBWBgEtUBNnz7dPWG5gbh5Qq3P9o1ArGnu3LnuyUbPaf4/KtCShXFETFJm7BbbOFalrJ4Q/nnz5sW5B4atJa18eVKzkoOI7es0plFhPXBzchVrMVaLI3eW++d0Up0MCZTg1pRKW7Stukz+Q/aYCjxkZ4n7cq3wACO0EtsiFbQCxfKf+ArbGOwEdFM0/glk4twm1V+nTp1rDqIky4bwEPRmijLxHuJ4CBTvKYW88ZkJ5d+mTTFeKgaOwvFdGzXto4Zq3vh1dRi7VOsOHtfuZWPV683merNxQzV4s68GzNwkK5SJGzDlEk6gYoMVNwmZ2IxHBlygjkfeBMsmfaNJk77T1KlTNHXyBH0debFxwX311ThNmDxLC9ftjdYFxZOVIQf+7gRM9DD+AaHmPeG9YR7/pRBA9zu9WaKT8cQi4A968xqZOi90qMRfRX0eK8ErWg0MT0Cskkkx+Na4ntjZxFZ/84AL1J+R4tE234O6P01yJUt2p5KlTKd7I7cfbEGyZMmotCnS65FKnTTij8OKiFwdXi/cSvsH4iO0r8UMyJthnIdOAMRsyLDQh9wPPhaEnTYmtDNh2+Sve/MHvRE3r7Q/JvCObYFtJj9vuI1pDzYoROdzQqRKly7tHiixsd0LuED9FRGhLYt/1Iz3S+r+PEX0YL1B+mHJElfCsGTJVA2sX1D5bkuuXOU+0Mj/nbrmSoqbjAJgsknchATIrRf1ebipR48e7XwqtHD1dy9YunSpi9ExrJHtEstxauR4Dac3on+9EpS4hkA/VfSIKBkjm2nnffDA0XcNkeL6o9VPTImzGNSJ7+qrZJmXVLbnKl24+PtrwxB1fiK1UiR7RNVHbtTWaySHeKJit8cgyBM/1IcdRBeC2H5zI90CGFjJfylBYV4c4kTQm04BtAH28gRlhBOTKSs8L7cpNi5m3bp1rpqA2DDXGiv6mBA3AnXqoHaNfVlPlKiqUp3n6+Jc2zbN/6isCie9V0U/WKLfr+KeJ0NAATDBX578GMZIdRMUDveD1QXeJ9zzBLsRKLa/rJLYIlGNzpONbBztc/keYPWJ3+nSvy++Dn4WbCJc1P4yHWKNrAQp3bnS99jhnYPPj9gTDxeSGwkTJnSF4jEZwhCnAlXsqRdVtsevuqiBxuklGteooPLcnl/Vhv5Pmy9ZQbH1IM6EONFxke1dw4YN1aZNGydUuJvD/SCwTdcGulGy6uB98h+IFcXTrKw6dOjg6vJat27tvudKf1d8HnyeVMsTw+Bn5ynM05iYI69f6Xvs8NbBZ9i+fXsVL1783DVIfeyCBT/rlD/AfGCVZn77pUaPGuWM1aO+mKxJC7YJP3rEvv3av2u//HujOBKoQ9r1ZW2VKPa0Cr8xSv+NfCLyVOT4ZVRLNXiygAo894FGXRKDIqZCfISUN4ZBYisEd1n282fS4nb8c/jfD94f6qTYBnP43y+yYWzxvPze8XNxsOpDWPk97LMOvoPPjIPPj3uW/2/XoVPkrmeHjm77SQt61FC+vDmUKWtW10wya45iKvxqb42dO0X9O/XT0OE/yt8gKW4E6vQR7f76FZXPl0KJ70qnzNmyuSA3R9Y0hfV0nX6atGWvDl+SmWS5iBls4sSJbjIJs/ZxrGKtp9bMjosP3hcMjTyVeK/87xfxumB4z/gZOXr06OEOYo787Ff6Wju8ffDZcf1xLQ4dNkLTfpirX8e3VvdK6ZQ7R2nV7PO9Zqxc6YraV/46X/8d11a1H8mplHcWUdX3psmfs40bgfrrkP78so5KPfao7q/8rj6NvOi48DgGvVNHNcs8qlKN3tPHs//UwQtKelhBEWci/sBWj3ofO0662FFUjyt9v1cP/89MTI2Yhn3moXBEXoOnzihi5Rh9UvUupU91tx5/Z7YWXtqc4uhK/TT2HVVKW0F16o3XSt/LcRuDKllTz/a6pB3HkQX66o37lCZBYqV7Zqimbj12bv9pGEYosEeruz+vwskSKUnx1hq7w/fyZezTghbdNLjreC3wvRKnAnXlLJ50aH4XvXVvAiVNVEEt52y77LxxMVsXL9a3w0Zq5NivNWHClxozcpiG+rZHQ4YO0/DREzRu8Xb9aZObjHjnTOT9P0P9ns6mlIkid0pdlmuX78xlnJWOLVustb+v0jrfS3EjUDqpQxNfUYlSNfR0t2W6uN78mLZ997Zeuz+BbktTQa2mbrv6L2A45nTpoiqZ71GaO/+lWxLeoRT3ZFKW7Nld//HsWTIq/V2JlaBwM7Ues0o79528rjvfMALHSWnzELV6/D+6O2sVNfnuULR2SAEXqLNnzujUoZ3aOOwFFS5SQU+0m6Wtx4453w7HoXk91eHZ5Ep2Z2alenW05m85cbENwbiMo7t3a9Ps/upe6T4l+VdZvdx/mhasWeMmKK9ZPE2TWhZUlrRJlTRlMVV5a7KWnzGJMuKJsxHSgo6qnu/fujlXdTWfdkSno3E5Blyg9qxera4li6vIvUmU8JbEujVVThUoVMhVPnM8ku1OJbnrXqWtPVTfrT2sU7HfUiY0OTJPU994TPekbKD28/ZcvEravUgL+lTRY/ck0k13lFaVT3/WZntjjfjg7FFp7rt6Ls+tSoBATT3sLYE6tGWLxr/XVm3e7aCOHSOP91qqRfPmau473mr5ntr2naRxv3urFszzbJumr197RGnurqOW09Zf3knyxGpNbldIuW67TXcW7KCxm07I3mEj7jklbR+mdx9PrdtSlVO1r6IXwImjGJQR61xPoCKJmNVSjXMnUJJM5dRqzhHttZ2eES9s0IzXH1LmhOmVvdlUbbzWYn73Ev2xZrl+8WXKTKCClSgI1NmVA9SxTCLdkiavqo/YoS22hDLiie1TmqtB3iRKc29FvTnhV627QsvTkzuXa+mQBuo24HMNXfPPayZQwUoUBEpbxqnvS+mUIEV2Fe26QusCP8bMMK7ImZO7tWJYY72YLplSZ8mlav2WavGu84XG+zf/olkfPqG6rdur17yDOuQzbJtABStREajfPlfnZxMrYer7VfnzLZcVYhtGXHL2yDb9MbmXPq6cRqkz51D2fAVcKyCOQkWfVL0PP9fYFVu09QIfkglUsBIFgTr5Y1s1y5tAie8pqeYzj2iPJfKMeOe0jv36tQZ2a6v3Wrd2nTU42nburvFrzuCauggTqGDlegL112bN+ugJFUh+u1I8+ZEmbDhpk3eNoMMEKlg5MFffNimstCnrq+3cXRe7cw+v09rR9fVM1kS6KeUzKjdsjY5agaMRhJhABSGncOD/OlaDa+ZViqRV1WjsEq3ft0/7ODYv0/xPnlHh+5Ipye0P6Mm6o/WjjQQ3ghQTqCBkXs+eqpkrk9Inu1kJEiRR8kw5lSdfPtd1NF+e7MqaMqHuKt1CbUcu15pNh610yAhaTKCCkD9mzNCg9zvrw2491fvTburauaM6tG/vWq2279BRHbv20aiFf8q7IxEMI2qYQBmG4VlMoAzD8CwmUIZheBYTKMMwPIsJlGEYnsUEyjAMz2ICZRiGZzGBMgzDs5hAGYbhWUygDMPwLCZQhmF4FhMowzA8iwmUYRiexQTKMAzPYgJlGIZnMYEyDMOzmEAZhuFZTKAMw/AsJlCGYXgWEyjDMDyLCZRhGJ7FBMowDM9iAmUYhkeR/h+HSaydOlbSfgAAAABJRU5ErkJggg==)
exterior angle = sum of interior opposite angles is a property of triangles
sum of interior angles of a triangle = 180 degree
In the figure, if AB = AC,
and AE = AD, then x is equal to
![](data:image/png;base64,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)
exterior angle = sum of interior opposite angles is a property of triangles
sum of interior angles of a triangle = 180 degree
Statement- (1) : The tangents drawn to the parabola y2 = 4ax at the ends of any focal chord intersect on the directrix.
Statement- (2) : The point of intersection of the tangents at drawn at P(t1) and Q(t2) are the parabola y2 = 4ax is {at1t2, a(t1 + t2)}
Statement- (1) : The tangents drawn to the parabola y2 = 4ax at the ends of any focal chord intersect on the directrix.
Statement- (2) : The point of intersection of the tangents at drawn at P(t1) and Q(t2) are the parabola y2 = 4ax is {at1t2, a(t1 + t2)}
Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.
Statement- (2) : If P(t1) and Q(t2) are the ends of a focal chord of the parabola y2 = 4ax, then t1t2 = –1.
slopes at the two extremeties of a focal chord are : (t,-1/t)
this property is used to explain the behaviour of tangents and normals at the respective points.
Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.
Statement- (2) : If P(t1) and Q(t2) are the ends of a focal chord of the parabola y2 = 4ax, then t1t2 = –1.
slopes at the two extremeties of a focal chord are : (t,-1/t)
this property is used to explain the behaviour of tangents and normals at the respective points.