2021 Fall AMC 12B Problems/Problem 10
Contents
Problem
What is the sum of all possible values of between and such that the triangle in the coordinate plane whose vertices are is isosceles?
Solution
Let and We apply casework to the legs of isosceles
Note that must be the midpoint of It follows that so
Note that must be the midpoint of It follows that so
Note that must be the midpoint of It follows that or so or
Together, the sum of all such possible values of is
Remark
The following diagram shows all possible locations of
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Video Solution (Just 1 min!)
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Video Solution by TheBeautyofMath
https://www.youtube.com/watch?v=4qgYrCYG-qw&t=1304
~IceMatrix
See Also
2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 12 Problems and Solutions |
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