Question 106

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

Solution

Let sides of triangle be x,y,z

=> x = AB = a+b

y = BC = b+c

z = CA = a+c

Thus, semi perimeter(s) = $$\frac{AB + BC + CA}{2} = a+b+c$$

Area of $$\triangle$$ABC = $$\sqrt{s(s-a)(s-b)(s-c)}$$

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

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