benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABCD be a square of side length 2. Let points X,Y, and Z be constructed inside ABCD such that ABX,BCY, and CDZ are equilateral triangles. Let point W be outside ABCD such that …

Problem

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

problem

Let ABCDABCD be a square of side length 2. Let points X,YX, Y, and ZZ be constructed inside ABCDABCD such that ABX,BCYABX, BCY, and CDZCDZ are equilateral triangles. Let point WW be outside ABCDABCD such that triangle DAWDAW is equilateral. Let the area of quadrilateral WXYZWXYZ be a+ba+\sqrt{b}, where aa and bb are integers. Find a+ba+b.
Plain-text mathematical notation (without MathML)
Let ABCD be a square of side length 2. Let points X,Y, and Z be constructed inside ABCD such that ABX,BCY, and CDZ are equilateral triangles. Let point W be outside ABCD such that triangle DAW is equilateral. Let the area of quadrilateral WXYZ be a+√(b), where a and b are integers. Find a+b.
Original LaTeX notation
Let \(ABCD\) be a square of side length 2. Let points \(X, Y\), and \(Z\) be constructed inside \(ABCD\) such that \(ABX, BCY\), and \(CDZ\) are equilateral triangles. Let point \(W\) be outside \(ABCD\) such that triangle \(DAW\) is equilateral. Let the area of quadrilateral \(WXYZ\) be \(a+\sqrt{b}\), where \(a\) and \(b\) are integers. Find \(a+b\).

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
467b4383-5a8a-5f4f-8f85-602e3f328136
task_key
test--467b4383-5a8a-5f4f-8f85-602e3f328136
task_revision_id
1
config / split
/ test

Official source

initial import