Home Geometry Problems Art All Problems Circle 491-500 Circle Inscribed in a Square Solution / comment        By Antonio Gutierrez
Problem 491. Square, Right Triangle, Incircle, Inscribed Circle, Radius.
Level: High School, College, SAT Prep.

The figure shows a square ABCD of side a with the right triangles AEB, BFC, CGD, and AHD. If the incircles of AEB, BFC, CGD, AHD, and EFGH are equal, find the radius x.
Incircle or Inscribed circle of a polygon is a circle tangent to each side of the polygon.

Square, Right triangles, Circles
 

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.

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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