MathDB
Cyclic Quadrilateral with angle 90,90,30,150

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April 23, 2009
trigonometry

Problem Statement

ABCD ABCD is a cyclic quadrilateral. If \angle B \equal{} \angle D, AC\bigcap BD \equal{} \left\{E\right\}, \angle BCD \equal{} 150{}^\circ, \left|BE\right| \equal{} x, \left|AC\right| \equal{} z, then find ED \left|ED\right| in terms of x x and z z.
(A)\ \frac {z \minus{} x}{\sqrt {3} } \qquad(B)\ \frac {z \minus{} 2x}{3} \qquad(C)\ \frac {z \plus{} x}{\sqrt {3} } \qquad(D)\ \frac {z \minus{} 2x}{2} \qquad(E)\ \frac {2z \minus{} 3x}{2}