Home Geometry Problems Art All Problems Semiperimeter 341-350 View or post a solution 
Problem 344. Quadrilateral, Extension of sides, Circle, Tangent, Semiperimeter. Level: High School, College, SAT Prep.

The figure shows a quadrilateral ABCD. The extension of the sides are tangent to circle O at E, F, G, and H. If s is the semiperimeter of the quadrilateral, prove that s = AB + BC = AD + CD.
 

Quadrilateral, Sides Extension, Tsngent, Circle, Semiperimeter

 


 

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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