2017 AMC 10B Problems/Problem 21
Contents
[hide]Problem
In , , , , and is the midpoint of . What is the sum of the radii of the circles inscribed in and ?
Solution
We note that by the converse of the Pythagorean Theorem, is a right triangle with a right angle at . Therefore, , and . Since , the inradius of is , and the inradius of is . Adding the two together, we have .
Video Solution
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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