There are two circles with a common center at point O and radius OA and OB. On a triangle AOB

There are two circles with a common center at point O and radius OA and OB. On a triangle AOB, side AB is 3 cm and side OA is greater than side OB by 1 cm. The perimeter of triangle AOB is 12 cm. Find the length of the radius Find the diameter of a circle with a radius.

Let the radius of one circle be OВ = x cm, then the second – OA = x + 1 cm.

The triangle AOB has side AB = 3 cm, and its perimeter P = 12 cm.

Since the perimeter is the sum of all sides of the triangle, then for the triangle AОВ

P = OA + OB + AB or

P = x + 1 + x + 3 = 12.

Where from,

2x + 4 = 12;

2x = 8;

x = 4 cm – OВ side.

Side OA = 4 + 1 = 5 cm.

Thus, one circle has a radius of 4 cm, and a diameter, respectively, is 8 cm, and the second circle has a radius of 5 cm and a diameter of 10 cm.