# Telltale signs

Geometry Level 4

Consider an acute triangle $$ABC$$ with $$X$$ as the foot of the perpendicular from $$A$$ to $$BC$$. Let the circle $$\Omega$$ with $$AX$$ as the diameter intersect $$AB$$ and $$AC$$ at $$D$$ and $$E$$ respectively. Let $$BE$$ and $$CD$$ intersect circle $$\Omega$$ at $$E'$$ and $$D'$$ respectively. If the measures of the angles $$E'AX, EE'D', D'AX$$ and $$EBC$$ are $$a,b,c$$ and $$d$$ respectively, and $$\dfrac{\sin (a) \sin(b)}{\sin(c) \sin(d)} = \dfrac xy$$ for coprime positive integers $$x$$ and $$y$$, calculate $$x+y$$.

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