Find the area of a circle bounded by a circle passing through points A (0; 0), B (5; 0), C (0; -12).

Circle equation: (x – xO) ^ 2 + (y – yO) ^ 2 = r ^ 2.

Substitute the coordinates of the given points:

(0 – xO) ^ 2 + (0 – yO) ^ 2 = r ^ 2; (one)

(5 – xO) ^ 2 + (0 – yO) ^ 2 = r ^ 2; (2)

(0 – xO) ^ 2 + (-12y – yO) ^ 2 = r ^ 2. (3)

Subtracting from (2) (1) we define xO:

(5 – xO) ^ 2 – (xO) ^ 2 = 0;

xO = 2.5.

Subtracting from (3) (1) we define yО:

(-12y – yO) ^ 2 – (yO) ^ 2 = 0;

yO = -6.

The coordinates of the center of the circle O (2.5; -6).

Substitute in (1) and define r ^ 2:

(0 – 2.5) ^ 2 + (0 + 6) ^ 2 = r ^ 2;

r ^ 2 = 42.25.

Area of a circle S = Pi * r ^ 2 = 42.25 Pi.