Problem 299: 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. 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.
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."