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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 Problem 301, formula to prove.
 

Tangents to a circle 

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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