The radius of a circle circumscribed about a right-angled triangle ABC is 50, find the smallest leg of this triangle

The radius of a circle circumscribed about a right-angled triangle ABC is 50, find the smallest leg of this triangle if it is known that the lengths of the legs are 4: 3 angle C 90 degrees.

Given:
R = 50
ABC – triangle
Leg lengths 4: 3
∠С = 90 °
Find: The smaller leg of the triangle -?
Decision:
Consider ΔАВС:
∠C = 90
BC / AC = 4/3 = 4x / 3x
BC = 4x
AC = 3x
The radius of the circumscribed circle in a right triangle = 1/2 hypotenuse AB
Hypotenuse AB = 2 * R = 2 * 50 = 100
AB ^ 2 = BC ^ 2 + AC ^ 2
10000 = 16 * x ^ 2 + 9 * x ^ 2
10000 = 25 * x ^ 2
x = 20
AC = 3 * 20 = 60
BC = 4 * 20 = 80