2020 CAMO Problems/Problem 3

Problem 3

Let $ABC$ be a triangle with incircle $\omega$ , and let $\omega$ touch $\overline{BC}$ , $\overline{CA}$ , $\overline{AB}$ at $D$ , $E$ , $F$ , respectively. Point $M$ is the midpoint of $\overline{EF}$ , and $T$ is the point on $\omega$ such that $\overline{DT}$ is a diameter. Line $MT$ meets the line through $A$ parallel to $\overline{BC}$ at $P$ and $\omega$ again at $Q$ . Lines $DF$ and $DE$ intersect line $AP$ at $X$ and $Y$ respectively. Prove that the circumcircles of $\triangle APQ$ and $\triangle DXY$ are tangent.

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2020 CAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
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2020 CAMO Problems/Problem 3

Problem 3

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