Problem 301: Tangents to a circle, Secants, Major Arc.
Level: High School, College, SAT Prep.
In the figure, AB and AC are tangent to circle O at B and C,
respectively, and D is a point on the major arc BC. Lines BD and AC meet
at E, and lines DC and BA meet at F. If
BF = a, CE = b, and EF = x, prove that
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."