Three circles of radius a, b, c touch each other externally.

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Three circles of radius a, b, c touch each other externally. The area of the triangle formed by joining their centre is

1. √(a + b + c)abc
2. (a + b + c)√ab + bc + ca
3. ab + bc + ca
4. None of the above

Correct Option: A

Using Rule 1,

x = AB = a + b
y = BC = b + c
z = CA = a + c

∴ s =	AB + BC + CA	= a + b + c
	2

∴ Area of ∆ ABC
= √s(s - x)(s - y)(s - z)
= √(a + b + c)abc