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2016 Geometry #5

Source:

August 11, 2022
2016Geometry Test

Problem Statement

Let Γ1\Gamma_1 be a circle of radius 66, and let Γ2\Gamma_2 be a circle of radius 11. Next, let the circles be internally tangent at point PP, and let APAP be a diameter of circle Γ1\Gamma_1. Finally, let YY be a point on Γ2\Gamma_2 such that AYAY is tangent to it. Compute the length of PYPY.
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