Maths-
General
Easy
Question
In the figure, AD is a median to BC in
and
. and DE =
![x text , prove that end text b squared plus c squared equals 2 p squared plus 1 half a squared](data:image/png;base64,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)
The correct answer is: Hence proved
Solution :-
Aim :- Prove that ![b squared plus c squared equals 2 p squared plus 1 half a squared](data:image/png;base64,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)
Hint :- apply in pythagoras theorem on triangles AEB , AEC and AED Find
and
values .Now, add them and do necessary modification to get in terms of p and a.
Explanation(proof ) :-
As D is mid point BD = DC = BC/2 = a/2
Applying pythagoras theorem to triangle AEB we get ,
![A C squared equals E C squared plus A E squared not stretchy rightwards double arrow b squared equals left parenthesis x plus a divided by 2 right parenthesis squared plus h squared minus Eq 1](data:image/png;base64,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)
Applying pythagoras theorem to triangle AEC we get ,
![A B squared equals B E squared plus A E squared not stretchy rightwards double arrow c squared equals left parenthesis x minus a divided by 2 right parenthesis squared plus h squared minus Eq 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUwAAAATCAYAAAD7wTTJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABaZJREFUeNrtXG9knVcYP66JiigTMXVNiZqaqTETUdMvM1E1NaaiZiLUVE0/hH2omKkQ+1BT/VIVVRMlKqqqSlRFRY2KyYeZMNMPNVPyoaoiwrvz1O/a6dn5/95zzvsu58dD7rnnzf29z/Oc5znP8557GYuHCrLDZY3LIdZstI1vk3m3VZcFxQ+yo8PlLJf1wnfP8W6rLkuAKn6QHduF757lHZMTLcT5ltrqQwQ2X8zjvtsWoNq6ppLjGJfVwndP8o7J6QiXxy1eF9e4nA68dg3335YA1dY15YXzDgbZ5fKUyx9c7nA5IM05AOOOJsheNi7bQtlSSSVMJzFfXz03kbcNsTmtYZfWRoxw+VOwXw9Hudzi8gL2/VUTVD/i8ihjgHql4J7LDyqD+MBV90qcwkVvad4/hH8o4iKX68Lr97jcVQSufsOFi2qOjFR86+q5CbxZZk6h5WxTcIHLrGKcgtwklyG8fh/3OamY+wiBM3WAIp/caIgfsIDAqIOP7t/A21DICpeTmjk0viiNfSGMkYLucdmfwPlsXHRzZCcL5RtqsFA994t3zJ1lbE4/cjnX0mDZwe5yxHH+QU2A+pb9t38bGqAqz/V2syF+0M+A6aP7N3AVUfVrLlc0c77n8p00doPLBP4mRR1O5IA2Lro5IurwDTVYqJ77xVvEjKdjDyFoPcMOeRkJIJXt73P5RDE+zdQPgS7ivRjB7wcufwtl3EHLNWTzhYCWk4xxLg8yJP2eTw5zuYR730IAj+Gb/eB+DLYhG1HLbsrjno294HFkKMI7+OcqLCHTdFAekQOct/QVQnoQLr0IGxdxjg+HmAHTV88xeMsl4lP0cVyCJT2BncPiHEDAPZHQ9i/wuSqsQ6c9TBkSUl2QDS8jWXQc7GUqpU2+omo/DEAPqZP+EoIm3cfnuO8uAstgBN+sy5108huXD4RS+5Yjn3FT64f6aE+4vCs5n8oIm4ISXkq7udRw4bKpMWA3Q0kQque6vCtHmWPmhv48gkRO7Brem8DOh/CptAvrJyYRPOTK5rjhGt/e6z4uvxgS2U6GpL+JRDEkjW9h15katkS7wNR9yKqm7l9njRlpjBbPWUUZ8lLIcuSUj9E/ydEPsnER58Q0kKujhug5FRbAf9Gg7+dC+d3EgElYEcqw4Uj2fIgdiIhVS0nuc5SIdHyby2eGOTuJfbjnk4OKTcCrTGvKtt7+QvDzuc6q+8NMfdCVnO6ONDamyNqn0dNKrSwXLmMRdxm+2bmunmMH+go7SN0O82NmPs6SyvamkpyhJUPB5EhEu8tHa2wJTneUSIVRLFjTt3XkkjyFD+t8chwJJAds3Hc9r3PR/etFoHNY+diLqmn9FbJnarhwCWmyxwqYdfUcC649TCo3l1l+rBi49s7TXWIOR0Jq4Lnic9ctOp51TKrXFLs4VZB6kNiHSZ/XPcabEDC3NUmqCtX9GS4/Gd6/KfVlqH81pSjlJjMoy4WLak6OgNkPPcfCjKInpQI9rPi9AQFTd6xoFDv1QdzPExavr/ZMKvVmEah1pazLUSJ6WLXE9OdyRZyrUdWF+rDOJ2l8OpMv2Lg/VCTXYcV1TrqnowgblsUyLS102mFMCGXGl+gVDWRQlgsXcU6ugFlXz00C6XcOjrUf5e/RxBxUD0/I/vekAElP7n+OxIGOKl1FMKS+5SI+37USUuEuc3/S7fu0vR8Bc5mpH2rpxpsQMMdQkXRhqxPwnSpE90vs3+MgOtAHbQqvt4Qychs7o24mZblw2TKUwamCfF095+KtAj3dX0VvaCPjzoIe7vV6lANYtF3Nzj1W4rkA285it0lnEk/WCG6uvVzbVyNjrrd9HuOpAqZNZ/QQ+DZiRO8rtVWg7gsKWokm/vjGSKLPcfnxjYL+7KoLCv43+Ia19+fdQkF9yzPF9CVgFhQUFKSC98/f/QPAE1sN+9HvqgAAAdZ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PG1zdXA+PG1pPkI8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPj08L21vPjxtaT5CPC9taT48bXN1cD48bWk+RTwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1pPkE8L21pPjxtc3VwPjxtaT5FPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxRDI7PC9tbz48bXN1cD48bWk+YzwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+PTwvbW8+PG1vPig8L21vPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5hPC9taT48bW8+LzwvbW8+PG1uPjI8L21uPjxtc3VwPjxtbz4pPC9tbz48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1cD48bWk+aDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtaT5FcTwvbWk+PG1uPjI8L21uPjwvbWF0aD7t4sVKAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Applying pythagoras theorem to triangle AED we get ,
![A D squared equals E D squared plus A E squared not stretchy rightwards double arrow p squared equals x squared plus h squared minus Eq 3](data:image/png;base64,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)
Adding Eq 1 and Eq 2
We get ![b squared plus c squared equals left parenthesis x minus a divided by 2 right parenthesis squared plus h squared plus left parenthesis x plus a divided by 2 right parenthesis squared plus h squared](data:image/png;base64,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)
[By applying ![open left parenthesis a minus b right parenthesis squared plus left parenthesis a plus b right parenthesis squared equals 2 open parentheses a squared plus b squared close parentheses close square brackets](data:image/png;base64,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)
![not stretchy rightwards double arrow b squared plus c squared equals 2 h squared plus 2 open parentheses x squared plus left parenthesis a divided by 2 right parenthesis squared close parentheses](data:image/png;base64,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)
![b squared plus c squared equals 2 open parentheses h squared plus x squared close parentheses plus 2 open parentheses a squared over 4 close parentheses](data:image/png;base64,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)
Substitute Eq3 in the above condition
![b squared plus c squared equals 2 open parentheses p squared close parentheses plus 1 half a squared not stretchy rightwards double arrow b squared plus c squared equals 2 p squared plus 1 half a squared](data:image/png;base64,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)
Hence proved
Related Questions to study
Maths-
Maths-General
Maths-
Maths-General
Maths-
The Quadrilateral PQRS has angles at S,Q right angles and the diagonals PR, QS are perpendicular. Prove that SR = QR.
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)
The Quadrilateral PQRS has angles at S,Q right angles and the diagonals PR, QS are perpendicular. Prove that SR = QR.
![](data:image/png;base64,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)
Maths-General
Maths-
P and Q are points on the sides CA and CB respectively of a
right angled at c. Prove that ![AQ squared plus BP squared equals](data:image/png;base64,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)
![A B squared plus P Q squared](data:image/png;base64,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)
P and Q are points on the sides CA and CB respectively of a
right angled at c. Prove that ![AQ squared plus BP squared equals](data:image/png;base64,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)
![A B squared plus P Q squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAASCAYAAADxEzisAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAmNJREFUeNrtl1FEZFEYx6+RZCWSZGQtSdJDliSrhyxrJcmKrLFWMuzDyNqHWD31kEhPK71kZWWtmIckK5FkjdHLylqrh2GttQ/pJUkyEu3/4385PvfcO6emuYb+/Jg598y933z3O//zHc+7O12TS5AH7V71KNbYEyADDrzqU6yxF73qVcVjHwDfqjRZTrG/KyHzV+Av+A02QVLNSdIH2ipQBb73nIMseBow7znYBhf8Tc4yzzn2lzS9Gst1McIfamwWfDK+d4CvAUkst3QsteAZ+AO6jPF5sAF66U/CCDgG/eqeTrE3gp9gB7ywzJHxL2ps1BiTB22BhhvuUi4KikWUBlP8/BYsW34vFbavKsspdrlxCoyDJcucGfBeja2CQX6WB3beYlt30YyRGE9V1CR4CH6xomw6ZWU6x/6EpShqoTcFKcs3K0E8BivK864DuKuEZbm0TDWDAmgCc0xcmHb4P5xiF7/6zjfi68CS7YIy2cEyN44uKiiv6aFZ+2Yu1fUo4h6ycT3wylDac2zedEN3rgx2n0Z5m846jLDm8opzTpioWSOBCe6IYarhknRSp6WjHWC7YKoP7KqxV2AhhgqTWPYiknEWcY9R+q+TciFvV7cXKXqWqdfgYwwJS6lWJkgXEYafN/yrJL0BH0Kur4Eh4/simFBzVhh8pRO2yPjDtBoQr69p15WRZM9VHzInrRK6bpi87EZjbBxrY0jYunqZNrv5xzbJXynd4DM92nlLHo6Y08qdyNeJsVyLrMDWmM56Ekudg9cVjWNUxrtXyZKj3xHbqDRXyr0iVM/TyiEP5ZH6D3Doo/17ccZhAAAAn3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5BPC9taT48bXN1cD48bWk+QjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+KzwvbW8+PG1pPlA8L21pPjxtc3VwPjxtaT5RPC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbWF0aD4HSHVGAAAAAElFTkSuQmCC)
Maths-General
Maths-
In △ABC, ∠B=90∘ and is the mid point of BC. Prove that ![A C squared minus A D squared equals 3 B D squared](data:image/png;base64,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)
In △ABC, ∠B=90∘ and is the mid point of BC. Prove that ![A C squared minus A D squared equals 3 B D squared](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
Maths-General
Maths-
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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)
.
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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)
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Maths-General
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