The circle is inscribed with a square ABCD, for which the vertices B (9: 9) and D (-1; 3) are known. Find the center of the circle.

1. The coordinates of the two vertices of the square ABCD are known:

B (9; 9);
D (-1; 3).
It is necessary to find the coordinates of the center of the circle circumscribed around the square.

2. The center of the circumscribed circle coincides with the center O of the square, that is, with the point of intersection of the diagonals, which are halved by this point. Therefore, it is in the middle of the BD diagonal:

x (O) = (x (B) + x (D)) / 2 = (9 – 1) / 2 = 8/2 = 4;
y (O) = (y (B) + y (D)) / 2 = (9 + 3) / 2 = 12/2 = 6;
Circle center coordinates: O (4; 6).

Answer: O (4; 6).