Question 1
Let $ABC$ be a triangle and $D$ a point on side $BC$. A line through $D$ intersects side $AB$ at $X$ and ray $AC$ at $Y$. The circumcircle of $BXD$ meets the circumcircle $\omega$ of $ABC$ again at $Z\ne B$. Lines $ZD,ZY$ meet $\omega$ again at $V,W$, respectively. Prove $AB=VW$.
Proposed by Warut Suksompong, Thailand.
Newly drawn configuration:
Editorial convention: all named circles and intersections are well-defined, and each second circle intersection is distinct from the first.
Proposed by Warut Suksompong, Thailand.
Newly drawn configuration:
Editorial convention: all named circles and intersections are well-defined, and each second circle intersection is distinct from the first.