Difference between revisions of "2021 Fall AMC 12B Problems/Problem 10"
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<math>20^\circ</math>, <math>50^\circ</math>, <math>80^\circ</math>, and <math>230^\circ</math>. | <math>20^\circ</math>, <math>50^\circ</math>, <math>80^\circ</math>, and <math>230^\circ</math>. | ||
| − | Thus we have <math>20+50+80+230=\boxed{(\textbf{E} )380}</math>. | + | Thus we have <math>20+50+80+230=\boxed{(\textbf{E })380}</math>. |
Revision as of 03:37, 24 November 2021
Problem
What is the sum of all possible values of 
between 
and 
such that the triangle in the coordinate plane whose vertices are 
, 
, and 
is isosceles?
Solution 1 (Quick Look for Symmetry)
By inspection, we may obtain the following choices for which symmetric isosceles triangles could be constructed within the unit circle described:
, 
, 
, and 
.
Thus we have 
.
~Wilhelm Z
| 2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
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Followed by Problem 11 |
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