2017 AMC 10B Problems/Problem 21
Problem
In ,
,
,
, and
is the midpoint of
. What is the sum of the radii of the circles inscibed 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
.
See Also
2017 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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All AMC 10 Problems and Solutions |
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