TopsOJ Summer 2025 - Guts Round - Problem 15

Circle \omega is tangent to side AB at B of parallelogram ABCD, tangent to side CD at X, and is also tangent to side AD. \omega passes through side BC at Y, AB=2 and XD=1. XY can be written as \frac{a\sqrt{b}}{c} for relatively prime positive integers a and c, and a positive integer b not divisible by the square of any prime. Compute a+b+c.