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Omni-MATH / In how many different places in the xy-plane can a third point, R, be placed so that PQ=QR=PR if points P and Q are two distinct points in the xy-plane?

Problem

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problem

In how many different places in the xyxy-plane can a third point, RR, be placed so that PQ=QR=PRPQ = QR = PR if points PP and QQ are two distinct points in the xyxy-plane?
Plain-text mathematical notation (without MathML)
In how many different places in the xy-plane can a third point, R, be placed so that PQ=QR=PR if points P and Q are two distinct points in the xy-plane?
Original LaTeX notation
In how many different places in the $xy$-plane can a third point, $R$, be placed so that $PQ = QR = PR$ if points $P$ and $Q$ are two distinct points in the $xy$-plane?

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Source and history

task_id
a81b3f26-ef6d-5e54-aa80-9c9fc77e6397
task_key
test--a81b3f26-ef6d-5e54-aa80-9c9fc77e6397
task_revision_id
1
config / split
/ test

Official source

initial import