Problem 181

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Problem 181: (2015 AMC 12b, 13)

Quadrilateral $ABCD$ is inscribed in a circle with $\angle BAC=70^{\circ}, \angle ADB=40^{\circ}, AD=4,$ and $BC=6$. What is $AC$? $\textbf{(A)}\; 3+\sqrt{5} \qquad$ $\textbf{(B)}\; 6 \qquad$ $\textbf{(C)}\; \dfrac{9}{2}\sqrt{2} \qquad$ $\textbf{(D)}\; 8-\sqrt{2} \qquad$ $\textbf{(E)}\; 7$

Solution

Exercise 181: Solution

Quadrilateral $ABCD$ is inscribed in a circle with $\angle BAC=69^\circ,\angle ADB=42^\circ, AD=4, BC=8$. What is $AC$?

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