Problem 359. Cyclic quadrilateral, Angle bisector, Rhombus.
Level: High School, College, SAT Prep.
In the figure below, ABCD is a cyclic quadrilateral. Lines AB and DC meet at E, and lines AD and BC meet at F. The bisectors of angles AED and AFB meet the sides BC, AD, CD, and AB at points M, N, G, and H, respectively. Prove that HMGN is a rhombus.
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 ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."