# 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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