MathDB
MAA be simping for isosceles triangles this year

Source: 12B #10

November 17, 2021
AMCAMC 12AMC 12 B

Problem Statement

What is the sum of all possible values of tt between 00 and 360360 such that the triangle in the coordinate plane whose vertices are (cos⁡40∘,sin⁡40∘),(cos⁡60∘,sin⁡60∘),(\cos 40 ^{\circ}, \sin 40 ^{\circ}), (\cos 60 ^{\circ}, \sin 60 ^{\circ}), and (cos⁡t∘,sin⁡t∘)(\cos t ^{\circ}, \sin t ^{\circ}) is isosceles?
<spanclass=′latex−bold′>(A)</span> 100<spanclass=′latex−bold′>(B)</span> 150<spanclass=′latex−bold′>(C)</span> 330<spanclass=′latex−bold′>(D)</span> 360<spanclass=′latex−bold′>(E)</span> 380<span class='latex-bold'>(A)</span>\ 100 \qquad<span class='latex-bold'>(B)</span>\ 150 \qquad<span class='latex-bold'>(C)</span>\ 330 \qquad<span class='latex-bold'>(D)</span>\ 360 \qquad<span class='latex-bold'>(E)</span>\ 380
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