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2019 CNMO P2

Source: 2019 China North MO, Problem 2

February 21, 2020
geometry

Problem Statement

Two circles O1O_1 and O2O_2 intersect at A,BA,B. Diameter ACAC of ⊙O1\odot O_1 intersects ⊙O2\odot O_2 at EE, Diameter ADAD of ⊙O2\odot O_2 intersects ⊙O1\odot O_1 at FF. CFCF intersects O2O_2 at HH, DEDE intersects O1O_1 at G,HG,H. GH∩O1=PGH\cap O_1=P. Prove that PH=PKPH=PK.
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