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Problem 1086: Square, Circle, Arc, Center, Metric Relations
Level: High School, College, Math Education

The figure below shows a square ABCD of center O and arcs FE and GH of centers D and A passing through O, respectively. If OE = 5, find EH.

Square, Circle, Arc, Center, 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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