There is a right angle triangle inside a circle of diameter 18cm. Inside this triangle ,there is another circle of diameter 6 cm. Find the perimeter of the triangle.
Choose the correct choice from the following choices:
A) 24 cm  B) 36 * 2 ^ 1 / 2 cm  C) 36 cm  D) 54 cm  E) 42 cm

Rationale: 1 ) the radius of the incircle of a right triangle with legs a and b and hypotenuse c is r = ( a + b - c ) / 2 2 ) the radius of the circumcircle is half the length of the hypotenuse r = c / 2 3 ) thus the sum of the circumradius and the inradius is half the sum of the legs r + r = ( a + b ) / 2 from 2 nd rule c = 18 cm from 3 rd rule a + b = 2 * ( 9 + 3 ) = 24 cm hence perimeter a + b + c = 24 + 18 = 42 cm answer : e
Answer: E