\( D \) is a point on the side \( B C \) of an equilateral triangle \( A B C \), such that \( D ...

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\( D \) is a point on the side \( B C \) of an equilateral
triangle \( A B C \), such that \( D C=\frac{1}{4} B C \). Prove that
\[
A D^{2}=13 C D^{2} \text {. }
\]
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