Problem 299: Intersecting Circles, Common Chord, Secant, Midpoint, Congruence. Level: High School, College, SAT Prep.
In the figure, the congruent circles O and Q intersect at A and B. C is
the midpoint of chord AB. Lines DA and DB intersect circle Q at E and F,
respectively. Lines EC and FC intersect circle O at G and H,
respectively. Prove that chords
DG and DH are congruent.