MathDB

5

Part of 1998 National Olympiad First Round

Problems(1)

Cyclic Quadrilateral with angle 90,90,30,150

Source: 0

4/23/2009
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}
trigonometry