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Fear the Sphere

Source: 2018 AMC 12B #23

February 16, 2018
AMCAMC 12geometry3D geometrysphere2018 AMC 12B2018 AMC

Problem Statement

Ajay is standing at point AA near Pontianak, Indonesia, 0∘0^\circ latitude and 110∘ E110^\circ \text{ E} longitude. Billy is standing at point BB near Big Baldy Mountain, Idaho, USA, 45∘ N45^\circ \text{ N} latitude and 115∘ W115^\circ \text{ W} longitude. Assume that Earth is a perfect sphere with center CC. What is the degree measure of ∠ACB\angle ACB?
<spanclass=′latex−bold′>(A)</span>105<spanclass=′latex−bold′>(B)</span>11212<spanclass=′latex−bold′>(C)</span>120<spanclass=′latex−bold′>(D)</span>135<spanclass=′latex−bold′>(E)</span>150 <span class='latex-bold'>(A) </span>105 \qquad <span class='latex-bold'>(B) </span>112\frac{1}{2} \qquad <span class='latex-bold'>(C) </span>120 \qquad <span class='latex-bold'>(D) </span>135 \qquad <span class='latex-bold'>(E) </span>150 \qquad
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