benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Four points, A,B,C, and D, are chosen randomly on the circumference of a circle with independent uniform probability. What is the expected number of sides of triangle ABC for which…

Problem

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

problem

Four points, A,B,CA, B, C, and DD, are chosen randomly on the circumference of a circle with independent uniform probability. What is the expected number of sides of triangle ABCA B C for which the projection of DD onto the line containing the side lies between the two vertices?
Plain-text mathematical notation (without MathML)
Four points, A,B,C, and D, are chosen randomly on the circumference of a circle with independent uniform probability. What is the expected number of sides of triangle ABC for which the projection of D onto the line containing the side lies between the two vertices?
Original LaTeX notation
Four points, $A, B, C$, and $D$, are chosen randomly on the circumference of a circle with independent uniform probability. What is the expected number of sides of triangle $A B C$ for which the projection of $D$ onto the line containing the side lies between the two vertices?

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
6075e974-9e89-582d-89cf-0025a628c8c2
task_key
test--6075e974-9e89-582d-89cf-0025a628c8c2
task_revision_id
1
config / split
/ test

Official source

initial import