Three circles of radius a, b, c touch each other externally. The area of the triangle formed by joining their centres is: -Maths 9th

Three circles of radius a, b, c touch each other externally. The area of the triangle formed by joining their centres is: -Maths 9th
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(a) \(\sqrt{(a+b+c).a.b.c}\)As shown in the figure, AB = a + b, BC = b + c, CA = a + c∴ Area of ΔABC = \(\sqrt{s(s-AB)(s-BC)(s-CA)}\)where, s = \(rac{1}{2}\) (AB + BC + CA)= \(rac{a+b+b+c+c+a}{2}\) = a + b + c∴ Area of ΔABC=\(\sqrt{(a+b+c)[(a+b+c)-(a+b)][(a+b+c)-(b+c)][(a+b+c)-(c+a)]}\)= \(\sqrt{(a+b+c).a.b.c}\)
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