Find the coordinates of the circumcenter of the triangle whose vertices are `(A(5,-1),B(-1,5),` and `C(6,6)dot` Find its radius also.

Explanation

To find the circumcenter of the triangle with vertices \( A(5, -1) \), \( B(-1, 5) \), and \( C(6, 6) \), we will follow these steps:

### Step 1: Set up the equations for the circumcenter
The circumcenter \( O(x, y) \) is equidistant from all three vertices of the triangle. Therefore, we can set up the following equations based on the distances from \( O \) to each vertex:

1. \( OA^2 = OB^2 \)
2. \( OA^2 = OC^2 \)

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