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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.
 

Circles, Chords, Radius, Perpendicular

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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