An equilateral triangle of side 9 cm is inscribed in a circle. The radius of the circle is |
A) \[3\,\,cm\]
B) \[3\sqrt{2}\,cm\]
C) \[3\sqrt{3}\,cm\]
D) \[6\,\,cm\]
Correct Answer: C
Solution :
Let ABC be an equilateral triangle of side 9 cm. |
Let AD be its median, then \[AD\bot BC\]and |
\[BD=4.5\,\,cm\] |
\[AD=\sqrt{A{{B}^{2}}-B{{D}^{2}}}\] |
\[=\sqrt{{{9}^{2}}-{{\left( \frac{9}{2} \right)}^{2}}}=\frac{9\sqrt{3}}{2}cm\] |
Let O be the centroid of\[\Delta ABC.\] |
Then, \[\frac{AO}{OD}=\frac{2}{1}\] |
Radius \[=AO=\frac{2}{3}AD=\frac{2}{3}\times \frac{9\sqrt{3}}{2}=3\sqrt{3}\,\,cm\] |
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