benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABC be a triangle that satisfies AB=13,BC=14,AC=15. Given a point P in the plane, let P_(A),P_(B),P_(C) be the reflections of A,B,C across P. Call P good if the circumcircle of…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let ABCA B C be a triangle that satisfies AB=13,BC=14,AC=15A B=13, B C=14, A C=15. Given a point PP in the plane, let PA,PB,PCP_{A}, P_{B}, P_{C} be the reflections of A,B,CA, B, C across PP. Call PP good if the circumcircle of PAPBPCP_{A} P_{B} P_{C} intersects the circumcircle of ABCA B C at exactly 1 point. The locus of good points PP encloses a region S\mathcal{S}. Find the area of S\mathcal{S}.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle that satisfies AB=13,BC=14,AC=15. Given a point P in the plane, let P_(A),P_(B),P_(C) be the reflections of A,B,C across P. Call P good if the circumcircle of P_(A)P_(B)P_(C) intersects the circumcircle of ABC at exactly 1 point. The locus of good points P encloses a region S. Find the area of S.
Original LaTeX notation
Let $A B C$ be a triangle that satisfies $A B=13, B C=14, A C=15$. Given a point $P$ in the plane, let $P_{A}, P_{B}, P_{C}$ be the reflections of $A, B, C$ across $P$. Call $P$ good if the circumcircle of $P_{A} P_{B} P_{C}$ intersects the circumcircle of $A B C$ at exactly 1 point. The locus of good points $P$ encloses a region $\mathcal{S}$. Find the area of $\mathcal{S}$.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
98408fe4-5091-57dd-b763-d5f8f5079328
task_key
test--98408fe4-5091-57dd-b763-d5f8f5079328
task_revision_id
1
config / split
/ test

Official source

initial import