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GCD of sides

Source: RMO 2018 P1

October 7, 2018
greatest common divisorgeometrycircumcircle

Problem Statement

Let ABCABC be a triangle with integer sides in which AB<ACAB<AC. Let the tangent to the circumcircle of triangle ABCABC at AA intersect the line BCBC at DD. Suppose ADAD is also an integer. Prove that gcd⁡(AB,AC)>1\gcd(AB,AC)>1.
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