A circle with a radius of 1 cm is inscribed in a right-angled triangle so that it breaks the hypotenuse into

A circle with a radius of 1 cm is inscribed in a right-angled triangle so that it breaks the hypotenuse into two segments equal to 2 cm and 8 cm. Find the perimeter of this triangle.

given: triangle ABC
AM = 2 cm
VM = 8cm
r = 1cm
decision:
the circle touches the triangle at the point M, K, E. by the property of tangents drawn from one point – AM = AK = 2 cm, BM = BE = 8cm, SK = CE = r = 1cm (because the formed quadrangle SKOE is a square .)
AC = 2 + 1 = 3
BC = 8 + 1 = 9
AB = 2 + 8 = 10
P = 9 + 3 + 10 = 22 cm