# 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.
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