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computational, starting with intersecting circles

Source: December 2020 Ukraine Geometry Olympiad X p5 , XI p4

December 20, 2020
geometrycircles

Problem Statement

Let Γ1\Gamma_1, Γ2\Gamma_2 be two circles, whereΓ1 \Gamma_1 has a smaller radius, intersect at two points AA and BB. Points C,DC, D lie on Γ1\Gamma_1, Γ2\Gamma_2 respectively so that the point AA is the midpoint of the segment CDCD . LineCB CB intersects the circle Γ2\Gamma_2 for the second time at the point FF, line DBDB intersects the circle Γ1\Gamma_1 for the second time at the point EE. The perpendicular bisectors of the segments CDCD and EFEF intersect at a point PP. Knowing that CA=12CA =12 and PE=5PE = 5 , find APAP.