benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let acute triangle ABC have circumcenter O, and let M be the midpoint of BC. Let P be the unique point such that ∠BAP=∠CAM,∠CAP=∠BAM, and ∠APO=90^(∘). If AO=53,OM=28, and AM=75, co…

Problem

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

problem

Let acute triangle ABCABC have circumcenter OO, and let MM be the midpoint of BCBC. Let PP be the unique point such that ∠BAP=∠CAM,∠CAP=∠BAM\angle BAP=\angle CAM, \angle CAP=\angle BAM, and ∠APO=90∘\angle APO=90^{\circ}. If AO=53,OM=28AO=53, OM=28, and AM=75AM=75, compute the perimeter of △BPC\triangle BPC.
Plain-text mathematical notation (without MathML)
Let acute triangle ABC have circumcenter O, and let M be the midpoint of BC. Let P be the unique point such that ∠BAP=∠CAM,∠CAP=∠BAM, and ∠APO=90^(∘). If AO=53,OM=28, and AM=75, compute the perimeter of △BPC.
Original LaTeX notation
Let acute triangle $ABC$ have circumcenter $O$, and let $M$ be the midpoint of $BC$. Let $P$ be the unique point such that $\angle BAP=\angle CAM, \angle CAP=\angle BAM$, and $\angle APO=90^{\circ}$. If $AO=53, OM=28$, and $AM=75$, compute the perimeter of $\triangle BPC$.

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
46174ae0-0334-59d2-8a06-a10cc06a1ccb
task_key
test--46174ae0-0334-59d2-8a06-a10cc06a1ccb
task_revision_id
1
config / split
/ test

Official source

initial import