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Mathematics
Problem
Three circles of radii
a
a
a
,
b
b
b
,
c
c
c
(
a
<
b
<
c
a < b < c
a
<
b
<
c
) touch each other externally. If they have x-axis as a common tangent, then : [JEE-MAIN ONLINE-2019] (1)
1
a
=
1
b
+
1
c
\frac{1}{\sqrt{a}} = \frac{1}{\sqrt{b}} + \frac{1}{\sqrt{c}}
a
1
=
b
1
+
c
1
(2)
a
a
a
,
b
b
b
,
c
c
c
are in A. P. (3)
a
\sqrt{a}
a
,
b
\sqrt{b}
b
,
c
\sqrt{c}
c
are in A. P. (4)
1
b
=
1
a
+
1
c
\frac{1}{\sqrt{b}} = \frac{1}{\sqrt{a}} + \frac{1}{\sqrt{c}}
b
1
=
a
1
+
c
1
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