The figure below depicts triangle ABC, with points
A_{1}, B_{1}, and C_{1} located on BC, AC, and AB, respectively.
These points are chosen such that the inradii of triangles AB_{1}C_{1}, BA_{1}C_{1}, and
CA_{1}B_{1} are all equal to d.
Let r represent the inradius of triangle ABC, and r_{1} denote the inradius of triangle
A_{1}B_{1}C_{1}.
Prove that r_{1} = r  d.
The power of proof shines,
Inradius code revealed,
Triangles aligned.
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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.
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by Antonio Gutierrez
Add a solution to the problem 1037
Last updated: Sep 19, 2014
