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Length relations and circle tangent to angle bisector.

Source: Dutch Tst 2014 P3

July 17, 2014
geometry proposedgeometry

Problem Statement

In triangle ABCABC, II is the centre of the incircle. There is a circle tangent to AIAI at II which passes through BB. This circle intersects ABAB once more in PP and intersects BCBC once more in QQ. The line QIQI intersects ACAC in RR. Prove that ∣AR∣⋅∣BQ∣=∣PI∣2|AR|\cdot |BQ|=|P I|^2
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