Question

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Answer 1

Proof: In right triangle ADB and ADC, we have

AB²= AD² + BD²

AC²= AD² + DC²

[By pythagourus theorem]

: AB² - DC² = BD² - DC² = 9CD² - CD² ;

[: BD= 3CD]= 8CD²= 8(BC/4)²

[: BC= DB+CD

= 3CD+CD

= 4CD

: CD= ¼BC]

: AB²-AC²= BC²/2

=> 2(AB²-AC²)= BC²

=> 2AB²-2AC²= BC²

which is the required result. [ Hence proved]

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