Kathleen's triangles

Geometry Level 4

In rectangle \(ABCD\), \(AB=6 \) and \(BC= 8 \). Point \(C\) is reflected across diagonal \(BD\) to obtain \(C'\), and line \(BC'\) intersects \(AD\) at \(P\). If the ratio of the area of triangle \(\triangle BAP\) to the area of triangle \(\triangle BPD\) is \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b\)?

This problem is posed by Kathleen K.

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