MathLabs

Problem 1

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 Z≠BZ\ne B. The lines ZDZD and ZYZY intersect ω\omega again at VV and WW, respectively. Prove that AB=VWAB=VW.
Step 2 of 3: Find the second cyclic quadrilateral
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Z,D,C,Y cyclicZ,D,C,Y\text{ cyclic}
Detailed analysis

The equality of the two angles subtending segment ZY proves that Z,D,C,Y are concyclic.