Problem 298: Intersecting Circles, 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. Prove that
C is the midpoint of line DE.
Geometry problem solving
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."