Three circles of radii 4 cm, 6 cm and 8 cm touch each other pairwise externally. The area of the triangle formed by the line segments joining the centres of the three circles, is |
A) \[6\sqrt{6}\,c{{m}^{2}}\]
B) \[24\sqrt{6}\,c{{m}^{2}}\]
C) \[144\sqrt{13}\,c{{m}^{2}}\]
D) (d)\[12\sqrt{105}\,c{{m}^{2}}\]
Correct Answer: B
Solution :
From figure, AB = 12 cm, BC = 14 cm and CA = 10 cm |
Area of \[\Delta ABC\] |
\[=\sqrt{s\,(s-a)(s-b)(s-c)}\] |
\[=\sqrt{18\,(18-14)(18-12)(18-10)}\] |
\[\left[ \because s=\frac{a+b+c}{2} \right]\] |
\[=\sqrt{18\times 4\times 6\times 8}=24\sqrt{6}\,c{{m}^{2}}\] |
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