A semicircle is inscribed in the triangle, the radius of which is 12 cm. The center of this semicircle divides one of the sides

A semicircle is inscribed in the triangle, the radius of which is 12 cm. The center of this semicircle divides one of the sides of the triangle into segments of 15 and 20 cm. Determine the unknown sides of the triangle.

To solve this problem, we need to use the properties of the circle.

We know that if we lower the perpendicular to the legs, we get two similar initial triangles.

Sides of a small triangle:

(a + r, b + r, 35).

The sides of the larger:

(r, b, 20).

Let’s derive the proportion:

a / r = 3/4;

The initial triangle has sides 21, 28, 35.

semicircle length πr = 12π;

Answer: πr = 12π;