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In any triangle ABC, prove that AB^2 + A...

In any triangle ABC, prove that `AB^2 + AC^2 = 2(AD^2 + BD^2)` , where D is the midpoint of BC.

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To prove that \( AB^2 + AC^2 = 2(AD^2 + BD^2) \) where \( D \) is the midpoint of \( BC \) in triangle \( ABC \), we will use coordinate geometry. ### Step-by-Step Solution: 1. **Set Up the Coordinates**: - Let \( D \) be the midpoint of \( BC \). - Place points \( B \) and \( C \) on the x-axis for simplicity. Let: \[ ...
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