benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let B and C be two fixed points in the plane. For each point A of the plane, outside of the line BC, let G be the barycenter of the triangle ABC. Determine the locus of points A su…

Problem

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

problem

Let BB and CC be two fixed points in the plane. For each point AA of the plane, outside of the line BCBC, let GG be the barycenter of the triangle ABCABC. Determine the locus of points AA such that ∠BAC+∠BGC=180∘\angle BAC + \angle BGC = 180^{\circ}. Note: The locus is the set of all points of the plane that satisfies the property.
Plain-text mathematical notation (without MathML)
Let B and C be two fixed points in the plane. For each point A of the plane, outside of the line BC, let G be the barycenter of the triangle ABC. Determine the locus of points A such that ∠BAC+∠BGC=180^(∘).

Note: The locus is the set of all points of the plane that satisfies the property.
Original LaTeX notation
Let $B$ and $C$ be two fixed points in the plane. For each point $A$ of the plane, outside of the line $BC$, let $G$ be the barycenter of the triangle $ABC$. Determine the locus of points $A$ such that $\angle BAC + \angle BGC = 180^{\circ}$.

Note: The locus is the set of all points of the plane that satisfies the property.

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
72341379-e832-513a-ab7e-838ecc0e602e
task_key
test--72341379-e832-513a-ab7e-838ecc0e602e
task_revision_id
1
config / split
/ test

Official source

initial import