Question

Draw an equilateral triangle of side 5 cm and its circumscribed circle. Find the length of the radius.

• A. 2.9 cm
• B. 3.8 cm
• C. 2.0 cm
• D. 4.9 cm

Answer 1

The correct option is A

2.9 cm

Draw the perpendicular bisectors of any two sides of the triangle.

Let the perpendicular bisector of BC and AC be drawn which meet at point O.

Taking O as the centre and radius equal to OA (or OB or OC) draw the circle.

Since the triangle is equilateral the perpendicular bisector passes through the vertex.


Consider triangle OBM; OB is the circumradious

$cos\left({30}^{\circ }\right)=\frac{BM}{OB}$
$⟹\frac{\sqrt{3}}{2}=\frac{2.5}{OB}$
$⟹OB=\frac{5}{\sqrt{3}}=2.88$