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

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

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: How to Solve It


Moku hanga or Japanese Woodblock printing of problem 491

Mind Map: How to Solve It

See also:
Typography of problem 491 using iPad Apps.

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