Find the radius of a circle circumscribed about an isosceles triangle. AB = BC = 5 cm, AC = 4 cm.

From the condition it is known that the triangle given to us is isosceles with sides AB = BC = 5 cm, AC = 4 cm, and we need to find the radius of the circle described around it.

We will start by recalling the formula for finding the radius of the circumscribed circle.

R = abc / 4S,

first of all, we find the area of the triangle using Heron’s theorem.

S = √p (p – a) (p – b) (p – c), where p = (a + b + c) / 2.

Let’s start with the floor perimeter:

p = (5 + 5 + 4) / 2 = 14/2 = 7;

S = √ (7 * 2 * 2 * 3) = √84 = 2√21 cm.

R = (5 * 5 * 4) / 2√21 = 50 / √21 cm radius.