A circle has equation, $x^2+y^2+14x+4y-19=0$
A smaller circle of centre $C$ shares a common tangent $y=3-x$ at the point $P$
The radius of the larger circle is three times the radius of the smaller circle.
Find the equation of the smaller circle.
I've spent a while playing around with this question. I have manged to solve it through the use of a diagram but I cannot see a more... Mathematical solution.
Through "counting boxes" I found the equation to be $(x-1)^2+(y-6)^2=(2\sqrt2 )^2$
Any input is much appreciated. Thanks in advance.