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in Olympiad by (65.8k points)

Let ABC be a triangle with integer sides in which AB < AC. Let the tangent to the circumcircle of triangle ABC at A intersect the line BC at D. Suppose AD is also an integer. Prove that gcd(AB,AC) >1

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Assume b & c are coprime then 

both should be divisible by a which is not possible as b + c > a have b & c can’t be coprime.

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