The center of the circumscribed circle lies at the height of an isosceles triangle and divides the height

The center of the circumscribed circle lies at the height of an isosceles triangle and divides the height into segments equal to 5 cm and 13 cm.Find the area of this triangle

The center of the circle circumscribed about the triangle lies at the intersection of the middle perpendiculars:
BO = OA = 13;
BO = OA – the radius of the circumscribed circle;
Let’s use the Pythagorean theorem:
AP ^ 2 = AO ^ 2 – OP ^ 2;
AP = 12;
We know that the area of a triangle is half the height at the base. Let’s write the formula for the solution:
S = (1/2) * BP * AC;
S = 18 * 12;
S = 216.
Answer: S = 216.