# Second Point Of Intersection Of Circumcircles

Geometry Level pending

Let $$\triangle ABC$$ be a triangle with $$BC= 5, CA= 6, AB= 7.$$ Let $$D, E$$ be the midpoints of $$AB, AC$$ respectively. The circumcircles of $$\triangle BCD$$ and $$\triangle ADE$$ meet for a second time at $$X$$ ($$X \neq A$$). Given that $$AX^2= \dfrac{a}{b}$$ for some coprime positive integers $$a, b,$$ find the last three digits of $$a+b.$$

Details and assumptions

• This problem is inspired by a recent problem that appeared in the Chinese Girls Mathematical Olympiad 2014.
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