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Question -

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



Answer -

Given : In ∆ABC, ∠C = 90°
D is mid-point of BC
AD is joined
=> 4AD² = 4AC² + BC²
=> BC² = 4AD² – 4AC²
=> BC² = 4 (AD² – AC²)
Hence proved.

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