Circle and symmetry
Source: 0
April 23, 2009
symmetrygeometry
Problem Statement
Chord is perpendicular to the diameter of a circle. Let and be the midpoints of the arcs and , respectively. If AD\bigcap BE\equal{}\left\{G\right\}, AF\bigcap BC\equal{}\left\{H\right\} and m(AC)\equal{}\alpha, find the measure of angle in terms of .(A)\ 90{}^\circ \minus{}\frac{\alpha }{2} \qquad(B)\ 60{}^\circ \minus{}\frac{\alpha }{3} \qquad(C)\ \alpha \minus{}30{}^\circ \\ \qquad(D)\ 15{}^\circ \plus{}\frac{\alpha }{2} \qquad(E)\ \frac{180{}^\circ \minus{}2\alpha }{3}