benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABCD be an isosceles trapezoid with AD=BC=255 and AB=128. Let M be the midpoint of CD and let N be the foot of the perpendicular from A to CD. If ∠MBC=90^(∘), compute tan∠NBM.

Problem

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

problem

Let ABCDA B C D be an isosceles trapezoid with AD=BC=255A D=B C=255 and AB=128A B=128. Let MM be the midpoint of CDC D and let NN be the foot of the perpendicular from AA to CDC D. If ∠MBC=90∘\angle M B C=90^{\circ}, compute tan∠NBM\tan \angle N B M.
Plain-text mathematical notation (without MathML)
Let ABCD be an isosceles trapezoid with AD=BC=255 and AB=128. Let M be the midpoint of CD and let N be the foot of the perpendicular from A to CD. If ∠MBC=90^(∘), compute tan∠NBM.
Original LaTeX notation
Let $A B C D$ be an isosceles trapezoid with $A D=B C=255$ and $A B=128$. Let $M$ be the midpoint of $C D$ and let $N$ be the foot of the perpendicular from $A$ to $C D$. If $\angle M B C=90^{\circ}$, compute $\tan \angle N B M$.

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
dd878939-37f9-5b75-97aa-dcdf6e0f80e0
task_key
test--dd878939-37f9-5b75-97aa-dcdf6e0f80e0
task_revision_id
1
config / split
/ test

Official source

initial import