Problem 665: Intersecting Circles, Secant, Tangent, Angles, Mind Map

Online Geometry Problems

Level: High School, Honors Geometry, College Geometry

The figure shows the intersecting circles O and O', the common chord AB and the secant CAD. CE and DE are tangent to circles O and O' at C and D, respectively. Prove that the measure of angle ABE is equal the difference of measure of angles EDC and ECD.

  

Intersecting circles, tangent, secant, angle
  

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.

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