Question

Let \(ABC\) be a triangle such that \(AB = 7\), \(BC = 8\), and \(CA = 9\). There exists a unique point \(X\) such that \(XB = XC\) and \(XA\) is tangent to the circumcircle of \(ABC\). If \(XA = \tfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a + b\).

Answer 1

trivial by coordbash

Answer 2

imagien getting your problem bashed SO bad

Answer 3

what's your solution though? I don't understand what you mean

Answer 4

The answer is 61.

Answer 5

take ommc

Answer 6

take ommc

Answer 7

Congratulations to OREN for being bad and not even making OMMC tiebreakers!