What Is a Circle?
A circle is a two-dimensional shape defined as a set of points in a plane equidistant from a fixed centre point. It is a closed, rounded shape without any corners or edges. The edge of a circle is a curved line, while the centre is the point from which all points on the edge are equidistant. Examples of objects that have circular shapes include car tires and wall clocks.
Activity for Becoming Familiar with the Formal Definition of a Circle
This activity aims to improve students’ awareness and visualisation of the circle’s definition.
- Measuring tape
- Pen and paper
- Use tape to create a circle on the floor.
- Seat one student at the circle’s centre, and have other students sit anywhere on the circle’s edge.
- Use a measuring tape to determine the distance between the student at the centre and each student on the edge of the circle. Ask each student on the circle’s edge to register their distance on paper.
- Collect the pieces of paper and ask the below questions.
- Which part of the circle represents the student at the centre?
- On which part of the circle are the students sitting, excluding the one in the middle?
- What is the relationship between the measurements recorded on each student’s paper?
- The student in the middle represents the circle’s centre.
- Students, except those in the middle, are seated on the circle’s edge.
- The recorded measurements will be nearly equal. This is because all points on the circle are equidistant from the circle’s centre, demonstrating the circle’s definition as a set of points equidistant from a single point, the circle’s centre.
Parts of a Circle
Eight distinct components comprise a circle – diameter, radius, chord, circumference, arc, tangent, sector and segment. We will examine each of these parts to understand their definitions better.
The circumference is the measure of the boundary or perimeter of a circle, composed of several points that are equidistant from the circle’s centre.
A chord is a straight line that lies within a circle and touches two points on the circumference without intersecting the circle’s centre.
A tangent is a straight line outside the circle that only touches one point of the circumference. A tangent is a straight line described by an equation in the form y -b = m(x-a). Both point and gradient are required to find its equation. You are usually given the point where the tangent meets the circle. The gradient can be calculated using the fact that the tangent is perpendicular to the radius from the point it meets the circle.
A diameter is the distance between two points on the circumference passing through the centre.
A radius is a line that joins the centre of a circle to any point on its circumference. It is equal to half of the diameter of the circle. At the endpoint of a radius on the circle’s circumference, the radius is always perpendicular to the tangent. This means that the angle formed between the radius and the tangent is always 90 degrees.
An arc in a circle refers to a segment of the circle’s perimeter bounded by two points on the circle. It is a straight line that joins two points on the circle, and the section of the circle traced out by this line segment is referred to as an arc.
A sector of a circle is a portion of a circle enclosed between two radii and an arc.
A segment of a circle is a region bounded by a chord and an arc of the circle.