A circle inscribed in triangle ABC touches sides AB, BC and AC at points M, K and P, respectively.

A circle inscribed in triangle ABC touches sides AB, BC and AC at points M, K and P, respectively. Find the perimeter of the triangle ABC if AP = 5, BM = 6, CK = 7.

Points P, M and K are the points of tangency of the circle with the sides of the triangles.

Then, by the property of tangents drawn from one point, AR = AK = 5 cm, BP = BM = 6 cm, CM = СK = 7 cm.

Side length AB = AP + BP = 5 + 6 = 11 cm, BC = BM + CM = 6 + 7 = 13 cm, AC = AK + СK = 5 + 7 = 12 cm.

Let’s define the perimeter of the triangle ABC.

Ravs = AB + BC + AC = 11 + 13 + 12 = 36 cm.

Answer: The perimeter of triangle ABC is 36 cm.