benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABC be an acute triangle and let M be the midpoint of AC. A circle ω passing through B and M meets the sides AB and BC at points P and Q respectively. Let T be the point such t…

Problem

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

problem

Let ABCABC be an acute triangle and let MM be the midpoint of ACAC. A circle ω\omega passing through BB and MM meets the sides ABAB and BCBC at points PP and QQ respectively. Let TT be the point such that BPTQBPTQ is a parallelogram. Suppose that TT lies on the circumcircle of ABCABC. Determine all possible values of BTBM\frac{BT}{BM}.
Plain-text mathematical notation (without MathML)
Let ABC be an acute triangle and let M be the midpoint of AC. A circle ω passing through B and M meets the sides AB and BC at points P and Q respectively. Let T be the point such that BPTQ is a parallelogram. Suppose that T lies on the circumcircle of ABC. Determine all possible values of (BT)/(BM).
Original LaTeX notation
Let $ABC$ be an acute triangle and let $M$ be the midpoint of $AC$. A circle $\omega$ passing through $B$ and $M$ meets the sides $AB$ and $BC$ at points $P$ and $Q$ respectively. Let $T$ be the point such that $BPTQ$ is a parallelogram. Suppose that $T$ lies on the circumcircle of $ABC$. Determine all possible values of $\frac{BT}{BM}$.

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
1c50550c-ef86-57da-bb75-832bac1d9117
task_key
test--1c50550c-ef86-57da-bb75-832bac1d9117
task_revision_id
1
config / split
/ test

Official source

initial import