10.363 In an isosceles triangle with a base of 12 cm, a circle is inscribed, and three tangents are drawn to it such that they cut off three small triangles from the given triangle. The sum of the perimeters of the small triangles is 48 cm. Find the lateral side of the given triangle.
Solution.

![](https://cdn.mathpix.com/cropped/2024_05_21_f024bf2ff7725246f3bfg-226.jpg?height=409&width=1085&top_left_y=440&top_left_x=100)

Answer: $18 \mathrm{~cm}$.