In an isosceles triangle, the base is 24 cm, and the lateral side is 15 cm.

In an isosceles triangle, the base is 24 cm, and the lateral side is 15 cm. Find the radii of the inscribed and circumscribed circles of the triangle.

Knowing the lengths of the sides of the triangle, we determine its area by Heron’s theorem.

Let’s define the semiperimeter of the triangle. p = (AB + BC + AC) / 2 = (15 + 15 + 24) / 2 = 27 cm.

Then Savs = √p * (p – AB) * (p – BC) * (p – AC) = √27 * 12 * 12 * 3 = √11664 = 108 cm2.

Determine the radius of the inscribed circle.

r = S / p = 108/27 = 4 cm.

Determine the radius of the circumscribed circle.

R = (AB * BC * AC) / 4 * S = 15 * 15 * 24/4 * 108 = 12.5 cm.

Answer: The radius of the inscribed circle is 4 cm, circumscribed 12.5 cm.