benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABC be a triangle with AB<AC, incenter I, and A excenter I_(A). The incircle meets BC at D. Define E=AD∩BI_(A), F=AD∩CI_(A). Show that the circumcircle of △AID and △I_(A)EF are…

Problem

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

problem

Let ABCABC be a triangle with AB<ACAB < AC, incenter II, and AA excenter IAI_{A}. The incircle meets BCBC at DD. Define E=AD∩BIAE = AD\cap BI_{A}, F=AD∩CIAF = AD\cap CI_{A}. Show that the circumcircle of △AID\triangle AID and △IAEF\triangle I_{A}EF are tangent to each other
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB<AC, incenter I, and A excenter I_(A). The incircle meets BC at D. Define E=AD∩BI_(A), F=AD∩CI_(A). Show that the circumcircle of △AID and △I_(A)EF are tangent to each other
Original LaTeX notation
Let $ABC$ be a triangle with $AB < AC$, incenter $I$, and $A$ excenter $I_{A}$. The incircle meets $BC$ at $D$. Define $E = AD\cap BI_{A}$, $F = AD\cap CI_{A}$. Show that the circumcircle of $\triangle AID$ and $\triangle I_{A}EF$ are tangent to each other

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
9e10c58c-6cbc-51f7-b3b3-cfa2149ea2da
task_key
test--9e10c58c-6cbc-51f7-b3b3-cfa2149ea2da
task_revision_id
1
config / split
/ test

Official source

initial import