benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABC be a triangle with AB equal{} AC . The angle bisectors of ∠CAB and ∠ABC meet the sides BC and CA at D and E , respectively. Let K be the incentre of triangle ADC. Suppose …

Problem

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

problem

Let ABC ABC be a triangle with $ AB \equal{} AC$ . The angle bisectors of ∠CAB \angle C AB and ∠ABC \angle AB C meet the sides BC B C and CA C A at D D and E E , respectively. Let K K be the incentre of triangle ADC ADC. Suppose that $ \angle B E K \equal{} 45^\circ$ . Find all possible values of ∠CAB \angle C AB . [i]Jan Vonk, Belgium, Peter Vandendriessche, Belgium and Hojoo Lee, Korea [/i]
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with $ AB \equal{} AC$ . The angle bisectors of ∠CAB and ∠ABC meet the sides BC and CA at D and E , respectively. Let K be the incentre of triangle ADC. Suppose that $ \angle B E K \equal{} 45^\circ$ . Find all possible values of ∠CAB .

[i]Jan Vonk, Belgium, Peter Vandendriessche, Belgium and Hojoo Lee, Korea [/i]
Original LaTeX notation
Let $ ABC$ be a triangle with $ AB \equal{} AC$ . The angle bisectors of $ \angle C AB$ and $ \angle AB C$ meet the sides $ B C$ and $ C A$ at $ D$ and $ E$ , respectively. Let $ K$ be the incentre of triangle $ ADC$. Suppose that $ \angle B E K \equal{} 45^\circ$ . Find all possible values of $ \angle C AB$ .

[i]Jan Vonk, Belgium, Peter Vandendriessche, Belgium and Hojoo Lee, Korea [/i]

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
7c743b0a-ebb4-5d82-bdcc-416920867db7
task_key
test--7c743b0a-ebb4-5d82-bdcc-416920867db7
task_revision_id
1
config / split
/ test

Official source

initial import