# omnimath / omnimath_1167 - 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 In acute triangle $A B C$, let $D, E$, and $F$ be the feet of the altitudes from $A, B$, and $C$ respectively, and let $L, M$, and $N$ be the midpoints of $B C, C A$, and $A B$, respectively. Lines $D E$ and $N L$ intersect at $X$, lines $D F$ and $L M$ intersect at $Y$, and lines $X Y$ and $B C$ intersect at $Z$. Find $\frac{Z B}{Z C}$ in terms of $A B, A C$, and $B C$. ## 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