Problem 297: Intersecting Circles, Chord, Secant, Radius, Angle, Perpendicular. Level: High School, College, SAT Prep.

In the figure, the circles O and Q intersect at A and B. Q is a point on circle O and C is a point on circle Q. Lines AC and BC meet circle O at points E and D, respectively. Prove that lines QC and DE are perpendicular.