In an isosceles triangle, the lateral side is 15, and the base is 18. Find the radius of the inscribed and circumscribed circle?

From the condition it is known that in an isosceles triangle the side is 15 and the base is 18. And we need to find the radius of the inscribed and circumscribed circle.
Let’s remember the formulas for finding the radii:
The radius of the circumscribed circle: R = abc / 4S;
Inscribed circle radius: r = S / p.
Where p is the floor perimeter, which we find by the formula:
p = (a + b + c) / 2 = (15 + 15 + 18) / 2 = 24 cm.
And we will find the area of the triangle by Heron’s formula:
S = √ (24 * (24 – 15) * (24 – 15) * (24 – 18)) = 108 cm ^ 2.
R = (15 * 15 * 18) / (4 * 108) = 9.375 cm.
r = 108/24 = 4.5 cm.