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In an equilateral triangle ABC, D is a p...

In an equilateral triangle ABC, D is a point on side BC such that `B D=1/3B C`. Prove that `9A D^2=7A B^2`.

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To solve the problem, we need to prove that in an equilateral triangle \( ABC \), where \( D \) is a point on side \( BC \) such that \( BD = \frac{1}{3} BC \), it follows that \( 9AD^2 = 7AB^2 \). ### Step-by-Step Solution: 1. **Understanding the Triangle**: Let \( AB = AC = BC = a \) (since \( ABC \) is an equilateral triangle). 2. **Positioning the Points**: ...
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