This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2019 USMCA, 3
Tags: trigonometry , geometry , inversion , projective , angle chasing , length chase
Let $ABC$ be a scalene triangle. The incircle of $ABC$ touches $\overline{BC}$ at $D$. Let $P$ be a point on $\overline{BC}$ satisfying $\angle BAP = \angle CAP$, and $M$ be the midpoint of $\overline{BC}$. Define $Q$ to be on $\overline{AM}$ such that $\overline{PQ} \perp \overline{AM}$. Prove that the circumcircle of $\triangle AQD$ is tangent to $\overline{BC}$.