An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.
Since the inscribed triangle is equilateral, therefore the angles at all the points = 60°
Using the formula for inscribed circle,
2R = \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)
where R = radius of the circle; a, b and c are the sides of the triangle.
⇒ 2R = \(\frac{\sqrt{3}}{\sin 60}\)
2R = \(\frac{\sqrt{3}}{\frac{\sqrt{3}}{2}}\)
2R = 2
R = 1cm
There is an explanation video available below.
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