A circle touching both the coordinates axes, having centre in the first quadrant and also touching the line $4x+3y=12$  is given by $x^2+y^2-2cx-2cy+c^2=0$ . Find the sum of all possible values of c. 
 

A circle that touches the coordinate axes is given by
${(x-c)}^2+{(y-c)}^2=c^2$
This circle touches the line
$$\begin{gathered} 4x+3y=12i.e 4x+3y-12=0 \\ \Rightarrow \frac{|4c+3c-12|}{\sqrt{{\left(4\right)}^2+{\left(3\right)}^2}}=c \iff |7c-12|=5c \iff c=1,6 \\ The sum of all possible values of c=7 \end{gathered}$$




 The sum of all possible values of c=7