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Geometry

Source: Iran MO 2018, second round, day 2, P6

April 27, 2018
geometryIran 2nd Round

Problem Statement

Two circles ω1,ω2\omega_1,\omega_2 intersect at P,QP,Q . An arbitrary line passing through PP intersects ω1,ω2\omega_1 , \omega_2 at A,BA,B respectively. Another line parallel to ABAB intersects ω1\omega_1 at D,FD,F and ω2\omega_2 at E,CE,C such that E,FE,F lie between C,DC,D .Let X≡AD∩BEX\equiv AD\cap BE and Y≡BC∩AFY\equiv BC\cap AF . Let RR be the reflection of PP about CDCD. Prove that: a. RR lies on XYXY . b. PR is the bisector of XPY^\hat {XPY}.
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