Maths-
General
Easy
Question
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
.
The correct answer is: Hence proved
Solution :-
Aim :- Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
Hint :- let the side of equilateral triangle be x , then we get height of equilateral
triangle as
.Now , Find length of DE and apply pythagoras theorem in
Right angle triangle ADE to find length of AD in terms of AB.
Explanation(proof ) :-
In equilateral triangle all sides are equal
Let , AB = BC = CA = x
Given BD = ⅓ BC = x/3 ( BC is trisected at D)
n equilateral triangle ,the altitudes and medians coincide
so,AE is median also i.e E is midpoint of BC
BE = x/2
From diagram ,DE = BE - BD ![equals x over 2 minus x over 3 equals x over 6](data:image/png;base64,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)
We get height of equilateral triangle when side x is![fraction numerator x square root of 3 over denominator 2 end fraction](data:image/png;base64,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)
Applying pythagoras theorem on triangle ADE
We get, ![A D squared equals D E squared plus A E squared equals open parentheses x over 6 close parentheses squared plus open parentheses fraction numerator x square root of 3 over denominator 2 end fraction close parentheses squared](data:image/png;base64,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)
![A D squared equals x squared over 36 plus fraction numerator 3 x squared over denominator 4 end fraction equals fraction numerator 28 x squared over denominator 36 end fraction equals 7 over 9 x squared](data:image/png;base64,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)
Substitute x by AB as x = AB
![A D squared equals 7 over 9 A B squared not stretchy rightwards double arrow 9 A D squared equals 7 A B squared](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence proved
Related Questions to study
Maths-
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
Maths-General
Maths-
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Maths-General
Maths-
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Maths-General
Maths-
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 8-√48
Classify whether the following Surd is rational or irrational , justify 8-√48
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Maths-General
Maths-
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAACZCAYAAACCCsDnAAAV70lEQVR4nO3deVyU173H8c8s7IsIAiqKW1RcgJkRVK6ARq42GiVJm7SvNJp706ZJTNImL5u2N4kbVGNfzXKvEbfb9GVzkyZtoyYajYogoKBGibizqAyKC4vsMzAMM/PcPxQSt2gU5pnlvF8v/4BZnt/A18N5znnOcxSSJEkIgotRyl2AIPQEEWzBJYlgCy5JBFtwSSLYgksSwRZckgi24JJEsAWXJIItuCQRbMEliWALLkkEW3BJItiCSxLBFlySCLbgkkSwBZckgi24JBFswSWJYAsuSQTbxdTU1PD5559TV1cndymyUstdgNB9GhoaSE9P59ChQ4waNYqQkBC5S5KNaLFdRFtbG++//z6rV6+murqa1tZWuUuSlWixXUBjYyMZGRm88847SJJEU1MTTU1NcpclK9Fiu4DDhw+zYcMGDAYDAE1NTbS0tMhclbxEsF3AxIkTWblyJampqQQHBxMUFER9fb3cZclKdEVcgK+vL1qtFh8fH+bNm0dKSgp+fn7YbDaUSvdsu0SwXURJSQm1tbXMnz+f8ePHy12O7Nzzv7OLqa+v5+OPP2b48OFotVq5y3EIIthOrrS0lOeff54PP/yQoKAgPDw85C7JIYiuiJPLzs7myy+/pL29nfPnz8tdjsMQwXZyEyZMYOjQoVy5coVp06Z1fd94pZpao5Xg8DC8FQo8vVQyVml/IthOrk+fPgQHB/P6668zd+5cAIzVR1j7p/+lxBhAv1EjGBA5med+8oDMldqX6GM7uYKCAgIDA0lMTLz2HYmyvBwueY/jT/+ziKnDe2Oz2mStUQ6ixXZira2t5OTkEB0dTWRk5LXvKggb0J+qFZ+y8m+9eOLHP+LfQgJkrVMOosV2YidPnqS0tJTU1FRUqm/70BETZvPbRU9SuXc9b/zhD2SWXMbd9mMRwXZihYWFREREMGbMmO9810ZNXRuD4h9l3d8+5MWEYDLXbKKmXbYyZSG6Ik6qoaGB7du3k5ycTFBQ0HcekTj7dTaFF9SkTBuLZ/hgAgb1QamQrVRZiBbbSX3zzTc0NTUxadKkGx5R0C9Kyyj/WnZs/AeHK7x56pl/J9RTljJlI1psJ5WVlUVkZCQ6ne6GR5QMHj6cwcMfIEUCUKBws9YaRIvtlGprazl9+jQzZszAy8vrNs9SoFC4Z6hBBNspHT16lNraWiZOnCh3KQ5LBNvJWCwWNm7cSFxcHAMHDpS7HIclgu1kqqurKS4u5sEHHxRX8n0PEWwnk5mZCSC6IXcggu1EDAYDeXl5aLVa+vTpI3c5Dk0E24mUlpZy6tQpHn/8cRTuOtxxl0SwnUhhYSGDBg1i7Nixcpfi8ESwnUR7ezuZmZkkJyfTq1cvuctxeCLYTqKgoECMXf8AIthOYvfu3QwZMoTY2Fi5S3EKIthOoLKykn379jFjxgw8Pd3saqZ7JILtBA4fPozRaESj0chditMQwXZwZrOZbdu2kZSUxNChQ+Uux2mIYDu4y5cvo9frmTx5suiG/AAi2A4uLy8Pf3//WywoEL6PCLYDMxqN5ObmMnLkSHr37i13OU5FBNuBlZWVUVxczKxZs8QU+g8kgu3AcnNzGTJkiJhCvwci2A6qsbGRvLw84uLibliFLtwNEWwHdejQIQwGAykpKXKX4pREsB3U/v37iYyMZOTIkXKX4pREsB3QpUuXKCoq4uGHH8bb21vucpySCLYDOnr0KE1NTcTExMhditMSwXYwJpOJTZs2odFoeOAB97qndXcSwXYwp0+fRq/X8+CDD4qx6/sggu1gCgsLUSqVJCQkyF2KUxPBdiAtLS0UFBSQlJREcHCw3OU4NRFsB6LX6ykpKWHKlCluu6NudxE/PQeyd+9ehg0bdvvREJsNq8Xa9aXVYqLFYKTd+u1+BZLVjKGlmRajCat09euWlmbazJaeLt+hiNsIO4iWlhYyMzNJSkq69Sp08xW2f/Qppy1RPPvcNHwxcGDnZ3yaeYx+sbN5ec5UennCiQNb+cfmvdDvQZ7/ZQp1Rzbzz22F9NWmMCf1Ifr4use2eKLFdhAHDx6kqKiIK1euYDAYbnrcZqqh6FgRp4svYQVMDU2o+k1l/i8fxetcJqcaLNB2jvLa3jzxi9/z2q+mE2auorwxkMeffIYx/gbKL7fY/4PJRATbQRw8eJCIiAjOnDnDunXraG+/ftMYZeBofjx7FoN9PbHYwDswlLHD1Jw48jV1/Scwqo+apopSThVsZtO2bOrarHj37s/AgGa+/PwflLT6EhnmJ9Onsz/RFbGTxnPf8OWWLCpbFagkD4aOSuTh2fH4KqGqqoqcnBzmz59PVFQUb775Jv379+fJJ5+84V0kpM79v9Se0FLD+ZOnKW5VcfGKkTGjUnjlv8aS9cl/896H/qS99Cjjk39C1LiHUXv54uPlPndnFS22nfgE9qG17hS5p9sYPMyHnA+W8/GuYwAcPXIEi8VCTEwM0dHRPPbYY2zatIkrV67c9D6Ka/8A/Adoeen1N5gYWc/+skZAhW9If2b89Gn8m9u43NQOKi8CA3vh6+WBO033iGDbiVfvSEZGj2TI6Ak89sRTJMSoOHCqlHbgiy8+Z+jQoV1T6FqtlsbGRi5fvvydd5Awm0y0mUx0WAGbBVN7O61mE4MD+jIo2B8kC6Z2M801jUQ9EE7fgNtt4+H6RFfEbiQkSzvV5YfZvLGS/Yc6SHg1itqaGkpLy/jls892bULq5eWFUqnEZDJ1vdpWp2dP/tccv2DkQPlsdMoT/PWjLTS19WLazCeYGhVAWd6XrN+4C89BI/jZU/+BG3WpbyKCbTcKFAorTVVnKS73ZdKzr/Do9Gi2fPYJR48d48KFC7S3t+Pl5UVbWxtqtRp/f/+uVyt7R/KLBct4WgJPb188FAm88poGCQ/8A/xRKWFownT+EJOE0ssbfz9fGT+r/ESw7UbCInkxZPwjvPK7VHoBHWYz+fkFJCYmsnfvXry9vXnuuefYvn07YWFhDBo06NuXK9X4+n93T3QVvXpdf6222suHIC8fu3waRyeCbSdNFYXszy2kvLqWfYdimRE/iPOVlRQVFbFs2TJCQ0NZuHAhx48f5+zZs7z88sv4+rp3q3s/RLDtxDt4EE+8sIRZNhVh/a/eIyQzM5MBAwag1WoJCgoiLS2NV155hZCQELHW8T6JURE78QoMJypWi1YbQ0R4IM3NzeTm5l63Cj0mJoZ3330XSZJYv379dSePwg8jgi2ToqIiKisrb2qZdTodCxYsYM+ePaxevfqmGUjh7ohgyyQ/P5/Q0FCGDx9+02NarZbFixeTl5fHqlWrRMt9D0SwZXD58mX27NnDzJkzCQwMvOVzNBoNixcvFi33PRLBlsHJkycxmUwkJiZ+7/N0Oh3p6enk5OSwatUqzGaznSp0fiLYdiZJUtety6Kiou74/JiYGNLS0sjOziYjI0N0S+6SCLadVVRUcPLkSVJSUrqm0O9Ep9Px1ltvdfW5Ozo6erhK5yeCbWcFBQU0NTUxbty4H/S62NhY0tLSyMrKYuXKlaLPfQci2HZkNBrJy8sjMTHxnvZC12g0LF++nJycHHFCeQci2Hak1+s5deoUkydPvutuyI00Gg3Lli0jNzeXVatWiXDfhgi2He3evZuwsDBGjx59X+8TExPTNRSYkZFBW1tbN1XoOkSw7cRoNFJQUMD48ePp27fvfb+fTqdj8eLFFBQUsHbtWhHuG4hg28mRI0eorq5m1qxZ3faeWq22a/pdhPt6Ith2UlhYyIgRI7p9E1KdTsfChQvZu3cva9asEZM414hg20F1dTU7duxg0qRJ+Pl1/3qtznDn5uaSkZEhwo0Itl0UFhZiMpmIi4vrsWNotVqWLFkiRkuuEcHuYZIk8dVXXzFixIge309Gp9OxbNkysrKyWL16NRaLe92v77tEsHuYXq+noqKCWbNmoVb3/IKl6Oholi5dyo4dO1ixYoXbnlCKYPew/fv3YzKZiI+Pt9sxtVotf/7zn7tOKN2xWyKC3YNMJhM7d+4kKSmJ8PBwux47NjaWJUuWsHv3brecfhfB7kEXLlygqqpKtv1kNBoN6enpbnlCKYLdg7Zs2UJgYCAajUa2GjoXK7jbShwR7B5SV1dHXl4eWq321jdyt6PY2FgWLFjQ1XK7wwmlCHYPKSoq4vz588ycOVPuUgCIi4sjLS2N/Px81qxZ4/LhFsHuAZIksX///rte/mUvGo2GBQsWkJeX5/LXlohg94C6ujoKCgqYOnUqPj6OdS89nU7HokWLXP7aEhHsHpCXl4dCoSApKUnuUm5p3LhxLFq0iOzsbJddQymC3c0sFgtZWVlERUUxYMAAucu5LY1Gw9KlS9m1a5dL3tpBBLubnTlzhhMnTvDQQw/JXcoddc5Q7tq1i4yMDJe6tkQEu5sdOHAAT0/P229C6mDGjh3L0qVLycrK4v3333eZ+5aIYHcjg8HA1q1bSUpK6pblX/ai1WpZtmxZ1wmlK4yWiGB3o/Lycmpra0lJSZFlCv1+dN4IMzc3l7Vr1zp9yy2C3Y3y8/MZNmwY48ePl7uUe6LRaFi4cCF79uxx+qsCRbC7SX19Pfv37yc5ORkvL+fdhi4uLo5FixY5fbhFsLvJ4cOH0ev1TJgwQe5S7lvn6vecnBzWrFnjlN0Stwy22Wigubmtc/NmwEpLQyNt7dZrX0sYai9yVn+R1o6rz2ptqqasrIyqRuN3XndVR0cHO3fuZPTo0QwePNg+H6KHjRs3jrS0NHJzc52y5Xa7YJvrTrJi4eus+qiAdgnAwtkDG3lt3kLyTzUC0HqhkM/Wv8uKjDWszy2hzVBHXvYmPvy/D9mQmU21wXrde1ZVVZGfn098fLzDTaHfD41Gw6JFi7oWKzjTaInbBVvh4YGnpwfWZlNXy6sK8MPDbKHDZAXaKdiyD9PQ2bz+28dp3ZPP6fJztHoMJDU1lUjPNq40Xz9Lt2/fPvz9/Zk8ebLdP09P0+l0pKWldV045SzT724XbI/A4STH6whWK5EkADWDx0xi4vBI1BJgrueoqYOAiFH0C+vDAOUh9MowhgQ08K/P/kWNbyTDwr9tla1WK/v27WPUqFHdfjMcR9EZ7l27drFy5UqnmKF0w30eJaw2K7brOsoWLDYbKECydGBQ2fD18QaaQdlOh8IL3ZS56KbMvendKioqOHfuHK+++qpdVqHLJTY2lqVLl/LGG2+gVCp58cUX8fT0lLus23K7FhsUKJQqVCoV386hKFEpr36t8Pajv0lJc30dVpOZ+uYQevvcPrAHDx7E19eXsWPH2qV6Oel0Ot5++22ys7NZvXq1Q3dL3C/YliYqK/RUXCin1ni12TbUXKT8vJ5zly9iUYaQPLoPTSU72Z7zNc0jk9D0u/XOXkajkc2bNxMdHX1PN3J3RtHR0SxZsqRrZwVHHQp0u2CbrtTSYFPhE2aiqtkI2Kg+cwHVwCBM5ks0dEDUjIeJD1dw6oKCRx6ZToiPCslmo66urusGOJWVlWRnZ1NVVXXH3b9czbhx40hPT2fv3r0OuxJHIUnSjcOywnUkjh07zoYNGyguLkatVqNQKLDZbJSUlDBmzBjWrVuHv7+/3IXaXVFREWlpaUyePJl58+bh7e0td0ldXPdsp5vs3n119m3gwIHMmTOHAQMGoFKpuHjxIunp6SQkJLhlqOHqDOWbb77JW2+9BeBQ4RbB/h7Hjx9nxYoVpKam8vTTT+Ph4dH1WGtrK56eniQnJ8tYofzi4+NZuHAh6enpKJVKXnjhBYe4Vsbt+th3q7m5mYyMDMaOHcvcuXOvCzVcXdeo0+kYMWKETBU6js77c2dlZbF27VqHmH53+GDbrp20Wa3WOz+5G+n1ei5evMicOXNuGq+tr6+nsLCQ5ORkh/nTK7fOE8rOrfrkHgp02GDbbDb0ej1vv/02r732Gs3Nzbd8XkNDA9u2bWP9+vVUV1d32/GPHTvGsGHDbtkiZ2dnYzQa3W405E60Wi1//OMfu/bEkXMo0OH62G1tbRw5coRt27axc+dODh8+TFhYGLNnzyYkJASbzdb1XLVazdatW/nggw8wmUz85je/Yfr06SgUCu51sKfztXl5eTQ2NpKfn48kSUiShEKhwGKx8Omnn2I2mzl69Cienp73fCxXpFarSUhI4L333sNkMvHSSy/h6+tr9zocbrhvx44d/PrXv+bMmTNd3/P19WXSpEl4eXldFyKlUklpaSllZWUoFAo0Gg0RERHdEjSbzYYkSbfcaNRisaBUKlEqHfYPnmwUCgVKpRKj0cjAgQNZvny5LOs/HSrYkiRRU1PDgQMH2Lp1K9nZ2ej1eiIjI9m6dSvh4eHX9bWVSiXlej2f/P3vBAQE8POf/5zw8HBsVssN14Lcm9u1/J1ht9msOM5Pz/F4eHgSHByMUmn/9Z8OFezvslgsHDlyhI8//piioiI2bNhAaGjoDc+SMLUaaGgyoFKr8FSrsaHCNyAAb3UPtaY2K8bmZkw2Jf4BAXh5iFb7diSbBWNLC2aLDavNhsrTm16BAajskHOHDXYns9nMpUuXiIiIuGnIzdxQxrq/rqCozIrxYjXqkBD8fS30n/ErFjwyiXvbrfx7WI18nfkFn395gGarkiEx8Tzy1I8ZEWT/PqQzaK8r4aPlS/hnSTtDIsKxdhhI+cUinpg0Ao8eDrdqyZIlS3r2EPdHpVIRFBR0y75ue3MjJr9QHnk0FVNRDbqf/SfP/FSLweDNqMh+qLq1MbVS9MVf+Si/mjm//QNzZydQdWITn2RXMy5BS4DDnYbLT+3bhwBVFcdtI0h7fT6h+l1sPFjHxCmT6OVx59ffD6f+O+odPIjk+BSGhvjj4+OHv58fffuP59EJo+n2nkh7JTuy99A3JoXYgUF4BfZl+tSHsJ3M4ZuKum4+mOvwCw3F3FxBzu6tnDWHMkGnIcgOq+ecOthKDzWenmqwXR2Ok64t9vL29aK771djMTZR09BBeFjvrh+ad0g4AQozdfW3HmMXQELCUneez//yF4rDE3nm6WkE2OG4Th3sLsqrQ0xKRc99HHVgHwb19ebc+Ut0LowyXNRTjx8RfYN77LhOT6EgPO4Rfv9f82g/sIdvzjTZ5bAuEey2pitU11VzqaoKQ3eM892KOoLZs6dy+dQWMo9UUHehhI07dhKcmErcQHn3mHFYkoW6M2ep1p8jKGoK02M6WLk6g8LTl+jo4SskXCDYVsrPHKXer5my4q8pvdTYY0caNuVJXpiZQPY7LzPt4cc5pUrkd79KJUicON5Se2MFxSW1eBsbOHHOxI+efpakXpf4astuLjX27LUkDj/cdzc6p7tBQpIU3d6/vpGh/ADvvL+MYr8ZvPHMY4wa2g9PF2giekLn70aS+Pb3IklICgU9+WtyiWDLod1YR9HuzXx9oZ3pP3uWUcE9PH4l/CAi2PdFwmaTUCiUPf5XQvhhRLAFlyR6hoJLEsEWXJIItuCSRLAFlySCLbgkEWzBJYlgCy5JBFtwSf8PPA5qxqHrIE4AAAAASUVORK5CYII=)
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
Maths-General
Maths-
Simplify √8 - √18 + √50
Simplify √8 - √18 + √50
Maths-General
Maths-
Maths-General
Maths-
Prove in the given figure, side QR of a
is produced to a point S.
If the bisector of
and
meet at the point T, then prove
![straight angle QTR equals 1 half straight angle QPR](data:image/png;base64,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)
![](data:image/png;base64,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)
Prove in the given figure, side QR of a
is produced to a point S.
If the bisector of
and
meet at the point T, then prove
![straight angle QTR equals 1 half straight angle QPR](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
In an equilateral triangle ABC,D is a point on the side BC , such that
. Prove that
![9 AD squared equals 7 AB squared](data:image/png;base64,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)
In an equilateral triangle ABC,D is a point on the side BC , such that
. Prove that
![9 AD squared equals 7 AB squared](data:image/png;base64,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)
Maths-General