benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABC be a triangle with AB=5,BC=8, and CA=7. Let Γ be a circle internally tangent to the circumcircle of ABC at A which is also tangent to segment BC.Γ intersects AB and AC at p…

Problem

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

problem

Let ABCA B C be a triangle with AB=5,BC=8A B=5, B C=8, and CA=7C A=7. Let Γ\Gamma be a circle internally tangent to the circumcircle of ABCA B C at AA which is also tangent to segment BC.ΓB C. \Gamma intersects ABA B and ACA C at points DD and EE, respectively. Determine the length of segment DED E.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=5,BC=8, and CA=7. Let Γ be a circle internally tangent to the circumcircle of ABC at A which is also tangent to segment BC.Γ intersects AB and AC at points D and E, respectively. Determine the length of segment DE.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=5, B C=8$, and $C A=7$. Let $\Gamma$ be a circle internally tangent to the circumcircle of $A B C$ at $A$ which is also tangent to segment $B C. \Gamma$ intersects $A B$ and $A C$ at points $D$ and $E$, respectively. Determine the length of segment $D E$.

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
e99783cc-d54c-5a1f-91b4-afaef47a5d2d
task_key
test--e99783cc-d54c-5a1f-91b4-afaef47a5d2d
task_revision_id
1
config / split
/ test

Official source

initial import