Question 77
In triangle $ABC$, points $P, Q, R$ lie on sides $BC, CA, AB$, respectively. Let $\omega_A, \omega_B, \omega_C$ denote the circumcircles of triangles $AQR, BRP, CPQ$, respectively. Given the fact that segment $AP$ intersects $\omega_A, \omega_B, \omega_C$ again at $X, Y, Z$ respectively, prove that $YX/XZ = BP/PC$.
(This problem was suggested by Zuming Feng.)
(This problem was suggested by Zuming Feng.)