# omnimath / omnimath_596 - 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 Given a point $p$ and a line segment $l$, let $d(p, l)$ be the distance between them. Let $A, B$, and $C$ be points in the plane such that $A B=6, B C=8, A C=10$. What is the area of the region in the $(x, y)$-plane formed by the ordered pairs $(x, y)$ such that there exists a point $P$ inside triangle $A B C$ with $d(P, A B)+x=d(P, B C)+y=d(P, A C)$? ## 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