Geometry classes, Problem 299: Intersecting Circles, Chord, Secant, Midpoint, Congruence. Math teacher Master Degree. College, SAT Prep. Elearning, Online math tutor, LMS.

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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.

Congruent Circles, Chord, Midpoint, Congruence

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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