Difference between revisions of "2017 AMC 10B Problems/Problem 21"
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Revision as of 15:01, 12 July 2020
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.