MathDB

Problem 11

Part of 2023 VN Math Olympiad For High School Students

Problems(1)

compute PR/PQ

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

3/25/2023
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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