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Omni-MATH / Let ω be the incircle of a fixed equilateral triangle ABC. Let ℓ be a variable line that is tangent to ω and meets the interior of segments BC and CA at points P and Q, respectivel…

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problem

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.
Plain-text mathematical notation (without MathML)
Let ω be the incircle of a fixed equilateral triangle ABC. Let ℓ be a variable line that is tangent to ω 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 ℓ.
Original LaTeX notation
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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Source and history

task_id
360c7e42-c4bc-582e-a9f9-1279f3e9442d
task_key
test--360c7e42-c4bc-582e-a9f9-1279f3e9442d
task_revision_id
1
config / split
/ test

Official source

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