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In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown.

 

  • The radius of the circle with center R is decreased so that
  • the circle with center R remains tangent to BC,
  • the circle with center R remains tangent to the other three circles, and
  • the circle with center P becomes tangent to the other three circles.

The radii and tangencies of the other three circles stay the same. This changes the size and shape of triangle ABC. r is the new radius of the circle with center R. r is of the form \(\frac{a+\sqrt{b}}{c}\). Find \(a+b+c\)

 Jun 28, 2019
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This question was asked and answered here: https://web2.0calc.com/questions/help_84836#r5

 Jun 28, 2019

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