The Hat Problem

Geometry Level 4

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

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

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