In triangles MPK angle M = 90 degrees, MP = 14, MK = 48. Find the radius of the circumscribed circle of this triangle.

Given: triangle MPK, angle M is 90 °, MP = 14, MK = 48.

Find: R is the radius of the circumscribed circle.

Decision:

Consider a triangle MPK, it is rectangular, since the angle M is equal to 90 °.
MP and MK are legs, we find the hypotenuse PK according to the Pythagorean theorem:
PK ^ 2 = MP ^ 2 + MK ^ 2,
PK ^ 2 = 14 ^ 2 + 48 ^ 2 = 196 + 2304 = 2500,
PK = 50.
The radius of a circle circumscribed about a right-angled triangle is equal to half of its hypotenuse. R = 50: 2 = 25.
Answer: 25.