A circle with a radius of 2 cm is inscribed in a right-angled triangle. The tangent point divides the hypotenuse

A circle with a radius of 2 cm is inscribed in a right-angled triangle. The tangent point divides the hypotenuse into two segments 5 cm and 3 cm long. Find the perimeter of the triangle.

given: r = 2 cm
AM = 5cm
ВM = 3 cm
find P
let the triangle ABC. 3 tangents at points-M, K, E
by the property of tangents drawn from one point – AM = AK = 5 cm, BM = BE = 3cm, СK = CE
since СKOE is a square, then СK = CE = r = 2cm
AC = 5 + 2 = 7 cm
BC = 3 + 2 = 5 cm
AB = 5 + 3 = 8 cm
P = 7 + 5 + 8 = 20 cm
answer: 20cm