Question

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

• A. $\sqrt{(a+b+c)abc}$
• B. $(a+b+c)$ $\sqrt{ab+bc+ca}$
• C. $ab+bc+ca$
• D. None of these

Answer 1

The correct option is A $\sqrt{(a+b+c)abc}$

$x=AB=b+c$

$y=BC=a+b$

$z=AC=a+c$

Therefore,

Semiperimeter = $\frac{AB+BC+AC}{2}=\frac{2a+2b+2c}{2}=a+b+c$

Area of $△ABC=\sqrt{s(s-x)(s-y)(s-z)}$$=\sqrt{(a+b+c)abc}$