Again With The Tangent Circles?Level pending
Consider the following circles: \(\Gamma_1\) is centered at \((1,0)\) with radius 1, \(\Gamma_2\) is centered at \((-1,0)\) with radius 1, and \(\Gamma_3\) is centered at \((0,4)\) with radius 2.
Now consider all circles that are tangent to \(\Gamma_1\), \(\Gamma_2\), and \(\Gamma_3\). Find the sum of the distinct curvatures of these tangent circles.
Details and assumptions
- The curvature of a circle is the reciprocal of its radius.
- We are only summing distinct curvatures, so if there are two circles with the same curvature, only add their curvature once.