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An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of...

Mathematics
JAMB 2000

An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.

  • A. 2/3 cm
  • B. 2 cm
  • C. 1 cm
  • D. 3 cm
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Correct Answer: Option C
Explanation

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


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WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
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