Circles and Pythagoras

Topic Classification: Tags:
Topics: geometry, circles, pythagorean theorem Prerequisites: geometry
Supplies: Pedagogy:
Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
1-2
3-4
5-6
7-8
9-10
11-12
13-14
Problem

Let $m$ and $n$ be integers. If $K_1$ is a circle of radius $1/m^2$
and $K_2$ is a circle of radius $1/n^2$, and if $K_1$, and $K_2$,
are tangent to each other and both are tangent to the same line,
find the radius of the circle tangent to both $K_1$ and $K_2$ and
to the line that lies in the area enclosed by them.

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Contributer: TRD
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