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.
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."
How to Solve It, Interactive Mind Map
George Pólya's 1945 book "How to Solve It, A new
aspect of Mathematical Method", is a book
describing methods of problem solving. It
suggests the following steps when solving a
mathematical problem: (1) First, you have to
understand the problem. (2) After understanding,
then make a plan. (3) Carry out the plan. (4)
Look back on your work. How could it be better? Mind Map Help. To see a note: Hover over a yellow note button. To Fold/Unfold: click a branch. To Pan: click and drag the map canvas.
Problem Solving. Activate Flash plugin or
Javascript and reload to view the Mind Map of How to Solve It,
Interactive Mind Map, Elearning.

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