# Three circles of radii a, b, c (a < b < c) touch each other externally. If they have x-axis as a common tangent, then :

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Three circles of radii $a,\ b,\ c\quad(a<b<c)$ touch each other externally. If they have x-axis as a common tangent, then :

(1) ${1\over\sqrt a}={1\over\sqrt b}+{1\over\sqrt c}$

(2) $a,\ b,\ c$ are in A. P.

(3) $\sqrt a,\ \sqrt b,\ \sqrt c$ are in A. P.

(4) ${1\over\sqrt b}={1\over\sqrt a}+{1\over\sqrt c}$