A geometry problem by Soham Jorapur

Geometry Level pending

If a, b, c be the radii of three circles which touch one another externally, and r1 and r2 be the radii of the two circles that can be drawn to touch these three, is 1/r1 - 1/r2 = 2/a + 2/b + 2/c? State answer with a proof.

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