The height drawn to the base of the isosceles triangle is 9 cm, and the base itself is 24 cm.

The height drawn to the base of the isosceles triangle is 9 cm, and the base itself is 24 cm. Find the radii of the circle inscribed in the triangle and circumscribed about the triangle.

The HL height is also the median of the ABC Triangle, then AH = CH = AC / 2 = 24/2 = 12 cm.

The length of the hypotenuse AB is equal to:

AB2 = AH2 + BH2 = 144 + 81 = 225.

AB = BC = 15 cm.

The radius of the circumscribed circle around the triangle is: R = a * b * c / 4 * Sас = 15 * 24 * 15/4 * 108 = 5400/432 = 12.5 cm.

The semi-perimeter of triangle ABC is equal to:

ravs = (AB + BC + AC) / 2 = 15 + 15 + 24 = 54/2 = 27 cm.

Savs = AC * ВН / 2 = 24 * 9/2 = 108 cm2.

Also Saavs = p * r.

Then: r = Savs / p = 108/27 = 4 cm.

Answer: r = 4 cm, R = 12.5 cm.