# omnimath / omnimath_563

- 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 $\triangle A B C$ be a triangle inscribed in a unit circle with center $O$. Let $I$ be the incenter of $\triangle A B C$, and let $D$ be the intersection of $B C$ and the angle bisector of $\angle B A C$. Suppose that the circumcircle of $\triangle A D O$ intersects $B C$ again at a point $E$ such that $E$ lies on $I O$. If $\cos A=\frac{12}{13}$, find the area of $\triangle A B C$.

## 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