A geometry problem by Yan Yau Cheng

Geometry Level 2

In \(\triangle ABC\), \(AB=10\) and \(AC=12\), \(D\) is a point on line \(BC\) such that line \(AD\) bisects \(\angle BAC\), The ratio \(\frac {BD}{CD}\) can be expressed as \(\frac pq\), where \(p\) and \(q\) are positive co-prime integers, find the value of \(p+q\)

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