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2020 USOJMO Problems/Problem 2

Revision as of 18:08, 23 June 2020 by Lcz (talk | contribs) (Created page with "==Problem== Let <math>\omega</math> be the incircle of a fixed equilateral triangle <math>ABC</math>. Let <math>\ell</math> be a variable line that is tangent to <math>\omega...")
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Problem

Let $\omega$ be the incircle of a fixed equilateral triangle $ABC$. Let $\ell$ be a variable line that is tangent to $\omega$ and meets the interior of segments $BC$ and $CA$ at points $P$ and $Q$, respectively. A point $R$ is chosen such that $PR = PA$ and $QR = QB$. Find all possible locations of the point $R$, over all choices of $\ell$.

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