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APMO 2015 P1

Source: APMO 2015

March 30, 2015
geometryAPMOcircumcircle

Problem Statement

Let ABCABC be a triangle, and let DD be a point on side BCBC. A line through DD intersects side ABAB at XX and ray ACAC at YY . The circumcircle of triangle BXDBXD intersects the circumcircle ω\omega of triangle ABCABC again at point ZZ distinct from point BB. The lines ZDZD and ZYZY intersect ω\omega again at VV and WW respectively. Prove that AB=VWAB = V W
Proposed by Warut Suksompong, Thailand
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