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Prove that some circles are concurrent.

Source: Moldova 2008 IMO-BMO Second TST Problem 3

March 29, 2008
geometrycircumcirclegeometry proposed

Problem Statement

Let ω \omega be the circumcircle of ABC ABC and let D D be a fixed point on BC BC, D≠B D\neq B, D≠C D\neq C. Let X X be a variable point on (BC) (BC), X≠D X\neq D. Let Y Y be the second intersection point of AX AX and ω \omega. Prove that the circumcircle of XYD XYD passes through a fixed point.
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