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Q. A circle is inscribed in a equilateral triangle of side a. The area of the circle is

J & K CETJ & K CET 2004

Solution:

In an equilateral triangle length of median $ CD=\frac{\sqrt{3}}{2}a. $
Also, centroid of triangle lies on the centre of circle.
$ \therefore $ $ OC=2\times \frac{\sqrt{3}}{2}a=\sqrt{3}a $
$ \therefore $ Area of circle = $ \pi {{(OC)}^{2}} $
$=3\pi {{a}^{2}}\,\,sq\,\,unit $

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