Geometry Problems, Online Education
Online Geometry Problem 863: Circumscribed trapezoid, Inscribed Circle, Tangent, Metric Relations. Level: High School, College, Mathematics Education

The figure below shows a circumscribed trapezoid ABCD (AD // BC) with BC, CD, AD, and AB tangent to the inscribed circle at points E, F, G, and H. DE and CG intersect at K. If CE = 2 and DG = 5, find KF.


Circumscribed trapezoid, Circle, Tangent, Metric Relations


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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