Question

In the given figure, triangle ABC is a right angle triangle with B = 90o and D is
mid point of side BC. Prove that:
AC2 = AD2 + 3CD2

Answer 1

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In △ABC, ∠B = 90° and D is the mid-point of BC. Prove that AC2 = AD2 + 3CD2.

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asked Jan 9, 2018 in Class X Maths by aditya23 (-2,160 points)

In △ABC, ∠B = 90° and D is the mid-point of BC. Prove that AC2 = AD2 + 3CD2.



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answered Jan 9, 2018 by priya12 (-12,638 points)

Given: In △ABC, ∠B = 90° and D is the mid-point of BC.

To Prove: AC2 = AD2 + 3CD2

Proof:

In △ABD,

AD2 = AB2 + BD2

AB2 = AD2 - BD2 .......(i)

In △ABC,

AC2 = AB2 + BC2

AB2 = AC2- BD2 ........(ii)   

Equating (i) and (ii)

AD2 - BD2 = AC2 - BC2

AD2 - BD2 = AC2 - (BD + DC)2

AD2 - BD2 = AC2 - BD2- DC2- 2BDx DC

AD2 = AC2 - DC2 - 2DC2 (DC = BD)

AD2 = AC2 - 3DC2

hope its help you