2017 AMC 8 Problems/Problem 22
In the right triangle , , , and angle is a right angle. A semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?
We can reflect triangle on line This forms the triangle and a circle out of the semicircle. Let us call the center of the circle
We can see that Circle is the incircle of We can use the formula for finding the radius of the incircle to solve this problem. The are of is The semiperimeter is Simplifying Our answer is therefore