The figure below shows a
triangle ABC where A_{1}, B_{1}, and C_{1} are on BC, AC, and AB,
respectively, so that the
incircles
of triangles AB_{1}C_{1}, BA_{1}C_{1}, and
CA_{1}B_{1} are equal. Prove that the
perimeter
of triangle A_{1}B_{1}C_{1} is
equal to the perimeter of triangle A_{2}B_{2}C_{2}.
(isoperimetric triangles).

Mind Map: George Pólya's 1945 book,
"How to Solve It"
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?
A mind map is a diagram used to visually organize information, knowledge, concepts or ideas.
See also:
Art of
Problem 1034: Delaunay Triangulation.
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Last updated: Sep 19, 2015
