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compute PR/PQ

Source: 2023 Viet Nam math olympiad for high school students D1 P11

March 25, 2023
geometryratio

Problem Statement

Given a triangle ABCABC inscribed in (O)(O) with 22 symmedians AD,CF(D,FAD, CF(D,F are on the sides BC,AB,BC, AB, respectively).). The ray DFDF intersects (O)(O) at P.P. The line passing through PP and perpendicular to OAOA intersects AB,ACAB,AC at Q,R,Q,R, respectively..
Compute the ratio PRPQ.\dfrac{PR}{PQ}.
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