benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / A circle passes through vertex B of the triangle ABC, intersects its sides ABand BC at points K and L, respectively, and touches the side AC at its midpoint M. The point N on the a…

Problem

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

problem

A circle passes through vertex BB of the triangle ABCABC, intersects its sides AB AB and BCBC at points KK and LL, respectively, and touches the side AC AC at its midpoint MM. The point NN on the arc BLBL (which does not contain KK) is such that ∠LKN=∠ACB\angle LKN = \angle ACB. Find ∠BAC\angle BAC given that the triangle CKNCKN is equilateral.
Plain-text mathematical notation (without MathML)
A circle passes through vertex B of the triangle ABC, intersects its sides ABand BC at points K and L, respectively, and touches the side AC at its midpoint M. The point N on the arc BL (which does not contain K) is such that ∠LKN=∠ACB. Find ∠BAC given that the triangle CKN is equilateral.
Original LaTeX notation
A circle passes through vertex $B$ of the triangle $ABC$, intersects its sides $ AB $and $BC$ at points $K$ and $L$, respectively, and touches the side $ AC$ at its midpoint $M$. The point $N$ on the arc $BL$ (which does not contain $K$) is such that $\angle LKN = \angle ACB$. Find $\angle BAC $ given that the triangle $CKN$ is equilateral.

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
a01abed5-c336-5c2a-8358-ff4e72f5cc1d
task_key
test--a01abed5-c336-5c2a-8358-ff4e72f5cc1d
task_revision_id
1
config / split
/ test

Official source

initial import