Question

In a right ∆ABC right-angled at C, if D is the mid-point of BC, prove that BC² = 4(AD² − AC²).

Answer 1

SOLUTION :  

Given : In a right ∆ABC ,∠C = 90°  and D is the mid-point of BC.

We have to prove that : BC² = 4(AD² - AC²)

In ∆ADC,

AD² = AC² + CD²

AD² = AC² + (BC/2)²

[D is the mid point of BC]

AD² = AC² + BC²/4

AD² = (4AC² + BC²)/4

4AD² = 4AC² + BC²

BC² = 4AD² - 4AC²

BC² = 4(AD² - AC²)

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Answer 2

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