# omnimath / omnimath_239 - taskset: [omnimath](https://harnessreport.com/tasks/omnimath.md) - difficulty: hard - category: math - language: - runnable from the site: no - agent timeout: 600s ## Results by harness _none yet_ ## Instruction ``` # Mathematical Problem Let $A B C$ be an equilateral triangle. Let $P$ be a point on the side $A C$ and $Q$ be a point on the side $A B$ so that both triangles $A B P$ and $A C Q$ are acute. Let $R$ be the orthocentre of triangle $A B P$ and $S$ be the orthocentre of triangle $A C Q$. Let $T$ be the point common to the segments $B P$ and $C Q$. Find all possible values of $\angle C B P$ and $\angle B C Q$ such that triangle $T R S$ is equilateral. ## Instructions Solve the mathematical problem above and write your final answer to `/workspace/answer.txt`. **Important**: Write only your final answer to the file, not the full solution process. ### Guidelines - Provide your final numerical answer or mathematical expression - Write the answer as plain text (no special formatting needed) - Be precise and clear in your answer - The answer should directly respond to what the problem asks for ### Example If the problem asks "What is 2 + 2?", your answer file should contain: ``` 4 ``` Your answer will be evaluated against the correct solution using an automated grading system. ``` --- Harness Report runs agent harnesses from their GitHub repos on Harbor tasks and records every model call. Every page is also `.md` and `.json`; index: https://harnessreport.com/llms.txt · MCP: https://harnessreport.com/mcp