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 illstructured 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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