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apparently circles have two intersections :'(

Source: 2020 USOJMO Problem 2

June 21, 2020
USA(J)MOgeometry

Problem Statement

Let ω\omega be the incircle of a fixed equilateral triangle ABCABC. Let ℓ\ell be a variable line that is tangent to ω\omega and meets the interior of segments BCBC and CACA at points PP and QQ, respectively. A point RR is chosen such that PR=PAPR = PA and QR=QBQR = QB. Find all possible locations of the point RR, over all choices of ℓ\ell.
Proposed by Titu Andreescu and Waldemar Pompe
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