MathDB

6

Part of 2022 Japan TST

Problems(1)

Three concurrent lines in a configuration with two circles

Source: Japan TST 2022, Day 2, P3

9/17/2022
Given is a circle Γ\Gamma with diameter MNMN and a point AA inside Γ\Gamma. The circle with center NN, passing through AA, meets Γ\Gamma at BB and CC. Let P,Q∈BCP, Q \in BC, such that ∠BAP=∠QAC\angle BAP= \angle QAC. The lines NP,NQNP, NQ meet Γ\Gamma at X,YX, Y, respectively. Prove that AM,PY,QXAM, PY, QX are concurrent.
geometry