Point on the Bisector

Geometry Level 4

\(ABC \) is a triangle with \( \angle BAC = 60^\circ, AB =5\) and \(AC = 25\). \(D\) is a point on the internal angle bisector of \(\angle BAC\) such that \(BD=DC\). What is \(AD^2\)?

Details and assumptions

It is \(\color{red} {\mbox{not} } \) stated that \(D\) lies on \(BC\). This assumption is not necessarily true.

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