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 ill-structured 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.