# 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 circles inscribed in the triangle and circumscribed about the triangle.

Since the triangle is isosceles, the height BH divides the base of the AC into equal segments. AH = CH = AC / 2 = 24/2 = 12 cm.

From the right-angled triangle ABH, by the Pythagorean theorem, we define the hypotenuse AB.

AB ^ 2 = AH ^ 2 + BH ^ 2 = 12 ^ 2 + 9 ^ 2 = 144 + 81 = 225.

AB = BC = 15 cm.

Let us determine the area and semiperimeter of the triangle.

Sас = АС * BН / 2 = 24 * 9/2 = 108 cm2.

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

Then the radius of the inscribed circle is: 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 = 75/8 = 12.5 cm.

Answer: The radius of the inscribed circle is 4 cm, the radius of the inscribed circle is 12.5 cm. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.