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Cyclic Quadrilateral with Isosceles Triangle

Source: 2015 AMC12B #13

February 26, 2015
AMC

Problem Statement

Quadrilateral ABCDABCD is inscribed inside a circle with ∠BAC=70∘,∠ADB=40∘,AD=4\angle BAC= 70^{\circ}, \angle ADB= 40^{\circ}, AD=4, and BC=6BC=6. What is ACAC?
<spanclass=′latex−bold′>(A)</span>3+5<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>922<spanclass=′latex−bold′>(D)</span>8−2<spanclass=′latex−bold′>(E)</span>7<span class='latex-bold'>(A) </span>3+\sqrt{5}\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>\frac{9}{2}\sqrt{2}\qquad<span class='latex-bold'>(D) </span>8-\sqrt{2}\qquad<span class='latex-bold'>(E) </span>7
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