A circle is inscribed in a triangle with sides 5 cm, 6 cm, 6 cm. Find the radius of this circle.

Since the two sides of the triangle, by condition, are equal, the triangle ABC is isosceles.

Then we will build the height BH, which will also be the median of the triangle ABC, then AH = CH = AC / 2 = 5/2 = 2.5 cm.

Let us determine the height of the ВН by the Pythagorean theorem.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 36 – 6.25 = 29.75.

BH = √29.75 cm.

Determine the area of the triangle ABC.

Sаvs = АС * ВН / 2 = 5 * √29.75 / 2 = 2.5 * √29.75 cm2.

Let’s define the semiperimeter of the triangle.

p = (6 + 6 + 5) / 2 = 17/2 = 8.5 cm.

Then the radius of the inscribed circle is:

R = Savs / p = 2.5 * √29.75 / 8.5 ≈ 1.6 cm.

Answer: The radius of the inscribed circle is 1.6 cm.