# omnimath / omnimath_38 - 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 $ABC$ be an acute scalene triangle and let $P$ be a point in its interior. Let $A_1$, $B_1$, $C_1$ be projections of $P$ onto triangle sides $BC$, $CA$, $AB$, respectively. Find the locus of points $P$ such that $AA_1$, $BB_1$, $CC_1$ are concurrent and $\angle PAB + \angle PBC + \angle PCA = 90^{\circ}$. ## 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