Tangents and Triangles

Geometry Level 4

The tangent at $$A$$ of the circumcircle of the triangle $$ABC$$ is drawn. The points $$D$$ and $$E$$ are constructed on it such that $$BD$$ is parallel to $$CA$$ and that $$CE$$ is parallel to $$BA$$. The lines $$BD$$ and $$CE$$ intersect the circle $$ABC$$ again at $$X$$ and $$Y$$ respectively.

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

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