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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