2021 Fall AMC 12B Problems/Problem 10
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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
~Steven Chen (www.professorchenedu.com) ~Wilhelm Z ~MRENTHUSIASM
2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
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