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
Denote ,
,
and
.
Case 1: .
We have or
.
Case 2: .
We have .
Case 3: .
We have .
Therefore, the answer is .
~Steven Chen (www.professorchenedu.com) ~Wilhelm Z ~MRENTHUSIASM
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