Problem 353. Tangential quadrilateral, Diagonals, Incircles, Inradii.
Level: High School, College, SAT Prep.
The figure shows a tangential
quadrilateral ABCD. Diagonals AC and BD meet at E. If r_{1},
r_{2}, r_{3}, and r_{4}, are the radii
of the incircles of triangles ABE, BCE, CDE, and ADE, 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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