Question

How many sides does a circle have?
(a) 10 sides
(b) 20 sides
(c) 300 sides
(d) infinite sides

Answer 1

Hint: A circle is a closed two-dimensional curve shaped figure, where all the points on the surface of the circle are equidistant from the centre point. A side is a line that is part of a flat figure made from straight lines. A circle has infinitely many points.

Complete step by step solution:
We have to find the number of sides that a circle has. Let us first understand what a circle is. A circle is a closed two-dimensional curve shaped figure, where all the points on the surface of the circle are equidistant from the centre point. We can represent a circle with centre O, geometrically as shown below.

We know that a side is a line that is part of a flat figure made from straight lines. Or we can say that all shapes are made up of line called sides. When three lines are joined, we will call that geometric shape a triangle. Similarly, when four sides are joined, we will get a square ( or rectangle, trapezium, rhombus or parallelogram). Let us inscribe a square, dodecagon(12 sided polygon) and pentacontagon(50 sided polygon) inside a circle as shown below.
 

From the above figure, we can see that when a square is inscribed in a circle, we can see many white spaces left. But when a dodecagon is inscribed, the white space is reduced. When we inscribed a pentacontagon, we can see that the white space has reduced a lot.
Similarly, when we join infinite sides, we will get a circle.

So, the correct answer is “Option d”.

Note: Students have a chance of making a mistake by assuming the number of sides of a circle as 0 because of the definition of a side. A side is also defined as the line segment that joins two vertices in a shape or two-dimensional figure. A circle has 0 vertices and 0 edges. So this definition of side validates the above solution. This definition of side is only applicable to polygons. We can conclude that a curve, ellipse, circle, parabola and hyperbola does not have sides.