# The Hat Problem

Geometry Level 4

Circle $$O$$ is drawn on plane $$K$$. On the same plane, $$\Delta ABC$$ with $$AB=13$$, $$AC=14$$, and $$BC=15$$ is drawn such that $$AB$$ and $$AC$$ are tangents to the circle at distinct points, and $$BC$$ contains the center $$O$$. If the area of circle $$O$$ can be expressed in the form $$\frac{a\pi}{b}$$, where $$a$$ and $$b$$ are positive coprime integers, find the value of $$a+b$$.

Draw a smiley face using the circle, and the title is justified. :)

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