Can You Generalize?

Geometry Level 4

\(ABC\) is a triangle with \(AB=360\), \(BC=240\), \(CA=180\). The internal and external angle bisectors of \(\angle CAB\) meet \(BC\) and \(BC\) produced at \(P\) and \(Q\) respectively. Find the circumradius of \(APQ.\)

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