 # Online Geometry Problem 823: Tangent Circles, Diameter, Perpendicular, Chord, Secant, Triangle, Area, Tangency Point. Level: High School, SAT Prep, College, Mathematics Education

 The figure below shows the circles O and Q tangent at A. QO extended cuts circle O at B and diameter CD is perpendicular to BQ at Q. E is a point on circle O and QE extended cuts circle O at F. If FE = 5 and EQ = 3, find the area of triangle BCD. 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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