In an isosceles triangle, the height drawn to the base is 6 cm and the side is 10, find the radius of the inscribed circle.

The height in an isosceles triangle drawn to the base divides the triangle into two equal right-angled ones.
The square of the leg of a right-angled triangle is 10 ^ 2 – 6 ^ 2 = 64. The leg is 8. the height has divided the base of the triangle in half, then the base is 8 * 2 = 16. The half perimeter of the triangle is (10 + 10 + 16) / 2 = 18. The area of the triangle is 1/2 * base * height = 1/2 * 16 * 6 = 48. The radius of the inscribed circle is 2 areas of the triangle divided by (base plus 2 sides) and is equal to (2 * 48) / (16 + 10 + 10) = 96/36 = 8/3 = 2 and 2/3.