Four points of the MKPO space form a rectangle MKPO find the area of the circle described

Four points of the MKPO space form a rectangle MKPO find the area of the circle described around it if OR = 17 ОМ = 15

Since the circle is circumscribed around a rectangle, the center of the circle coincides with the intersection point of the diagonals of the rectangle.

The diagonal of a rectangle is the diameter of the circumscribed circle, then in a right-angled triangle MOR, according to the Pythagorean theorem, we determine the length of the hypotenuse MP.

MP ^ 2 = OM ^ 2 + OP ^ 2 = 15 ^ 2 + 17 ^ 2 = 225 + 289 = 514.

MP = D = √514.

Determine the area of the circle.

S = n * D2 / 4 = n * 514/4 = n * 128.5 cm2.

Answer: The area of the circle is equal to n * 128.5 cm2.