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BE, CF, PR concurrent

Source: Junior Olympiad of Malaysia Shortlist 2015 G6

July 17, 2015
geometry

Problem Statement

Let ABCABC be a triangle. Let ω1\omega_1 be circle tangent to BCBC at BB and passes through AA. Let ω2\omega_2 be circle tangent to BCBC at CC and passes through AA. Let ω1\omega_1 and ω2\omega_2 intersect again at P≠AP \neq A. Let ω1\omega_1 intersect ACAC again at E≠AE\neq A, and let ω2\omega_2 intersect ABAB again at F≠AF\neq A. Let RR be the reflection of AA about BCBC, Prove that lines BE,CF,PRBE, CF, PR are concurrent.
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