Math, asked by madhvigumber1, 8 months ago

In A ABC, 2 B = 90° and D is the mid-point of BC.
Prove that BC? = 4 (ADP - AB)​

Answers

Answered by aaryanvartak30
1

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

Answered by khushalbaniya75
0

Answer:

2B=90°

then B =90°÷2

therefore. B= 45

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