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P on altitude and concurrent lines

Source: Moldova TST 2017, B3

March 6, 2017
geometry

Problem Statement

Let ω\omega be the circumcircle of the acute nonisosceles triangle ΔABC\Delta ABC. Point PP lies on the altitude from AA. Let EE and FF be the feet of the altitudes from P to CACA, BABA respectively. Circumcircle of triangle ΔAEF\Delta AEF intersects the circle ω\omega in GG, different from AA. Prove that the lines GPGP, BEBE and CFCF are concurrent.
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