Tangents and Triangles

Geometry Level 4

The tangent at AA of the circumcircle of the triangle ABCABC is drawn. The points DD and EE are constructed on it such that BDBD is parallel to CACA and that CECE is parallel to BABA. The lines BDBD and CECE intersect the circle ABCABC again at XX and YY respectively.

Given that BC=10BC = 10, find AX+AYAX + AY.

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