Quantitative Aptitude Ques 634

Question: An equilateral triangle of side 9 cm is inscribed in a circle. The radius of the circle is

Options:

A) $ 3cm $

B) $ 3\sqrt{2},cm $

C) $ 3\sqrt{3},cm $

D) $ 6cm $

Show Answer

Answer:

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=4.5cm $ $ AD=\sqrt{AB^{2}-BD^{2}} $ $ =\sqrt{9^{2}-{{( \frac{9}{2} )}^{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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