Home Geometry Problems All Problems Circle 481-490 Solution / comment        By Antonio Gutierrez
Problem 490. Tangent Circles, Arc, Radius, Circular Sector, Area.
Level: High School, College, SAT Prep.

The figure shows the circles of centers A, B, and C tangent at D, E, F. The measure of the arc DE is 130 degrees and the arc DF is 150 degrees. If the radius of circle C is 3, find the area of the circular sector ECF.

Circular sector area


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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