Math, asked by nikshep70, 6 months ago

15. In AABC, ZB = 90° and D is the mid-point of BC. Prove that :
(i) AC2 = ADP + 3CD2
(ii) BC2 = 4(AD2 - AB2)​

Answers

Answered by Akankshapatel763
8

Answer:

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

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