The figure shows the intersecting
circles O and O' at A and B and the secant CAD. CE and
DE are tangent to circles O and O' at C and D, respectively.
BE meets circle O' at F, DF extended meets CE at G. If CG = 5
and GE = 4, find DE.
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.