¶ 2017 AMC 10B Problem 21
Problem:
In , and is the midpoint of . What is the sum of the radii of the circles inscribed in and ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
By the converse of the Pythagorean Theorem, is a right angle, so , and the area of each of the small triangles is (half the area of ). The area of is equal to its semiperimeter, , multiplied by the radius of the inscribed circle, so the radius is . Similarly, the radius of the inscribed circle of is . The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions