benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABCD be a convex trapezoid such that ∠ABC=∠BCD=90^(∘),AB=3,BC=6, and CD=12. Among all points X inside the trapezoid satisfying ∠XBC=∠XDA, compute the minimum possible value of …

Problem

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

problem

Let ABCDA B C D be a convex trapezoid such that ∠ABC=∠BCD=90∘,AB=3,BC=6\angle A B C=\angle B C D=90^{\circ}, A B=3, B C=6, and CD=12C D=12. Among all points XX inside the trapezoid satisfying ∠XBC=∠XDA\angle X B C=\angle X D A, compute the minimum possible value of CXC X.
Plain-text mathematical notation (without MathML)
Let ABCD be a convex trapezoid such that ∠ABC=∠BCD=90^(∘),AB=3,BC=6, and CD=12. Among all points X inside the trapezoid satisfying ∠XBC=∠XDA, compute the minimum possible value of CX.
Original LaTeX notation
Let $A B C D$ be a convex trapezoid such that $\angle A B C=\angle B C D=90^{\circ}, A B=3, B C=6$, and $C D=12$. Among all points $X$ inside the trapezoid satisfying $\angle X B C=\angle X D A$, compute the minimum possible value of $C X$.

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
f708880a-112d-574e-9ff5-449ab18a067c
task_key
test--f708880a-112d-574e-9ff5-449ab18a067c
task_revision_id
1
config / split
/ test

Official source

initial import