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 \(a+b+c\).
+118689 Does anyone have any input for this one?
I have spent a lot of time looking.
If anyone else wants to step in, even with just thoughts, that would be good :)
Also
Does anyone know how to graph a cirlce (B) centred on the circumference of another cirlce (A) and moving on that arc?
(Like a planet going around the sun)
+118689 Thanks Rom,
I do not know how to do that but I did end up making the diagram.
I only know how to use Desmos and GeoGebra 
One trouble is, I actually do not understand what the question is asking.
Are a,b and c the side lengths of the triangle ?
Anyway, here are my graphs of the two most extreme r values. that is r=1 and r=0.8
radius = 1
radius 0.8
+33652 Here's my take on this:
I guess what is wanted is that a = -1, b = 5 and c = 2. However, this is a bit silly, as r can be expressed in an infinite number of ways simply by multiplying numerator and denominator by any positive number, p. Then we would have a = -p, b = 5p2 and c = 2p.
+118689 Thanks Alan, it always looks easy when someone else shows you how :)
It was sort of like that other circle one that you solved the other day. :)
I suppose I mainly wanted to graph it but I know my graph is not quite right anyway. I saw my error tonight.
Maybe I will fix it ...
