Find The Length

Geometry Level 5

Let ABC\triangle ABC be a triangle with side lengths BC=9,CA=8,AB=6.BC = 9, CA= 8, AB= 6. Let OO and II be the circumcenter and incenter of ABC\triangle ABC respectively. The incircle of ABC\triangle ABC touches BCBC at point D.D. Let XX be the second point of intersection of line AOAO and the circumcircle of AID\triangle AID (apart from AA). Given that AX=abAX = \sqrt{\dfrac{a}{b}} for some coprime positive integers a,b,a,b, find a+b.a+b.

Details and assumptions

  • The image shown is not accurate.

  • This problem is adapted from a Russia 10th grade geometry problem.

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