Points in a Plane with respect to a Circle in the Same Plane

All points in the same plane that are at an equal distance from a centre point form a circle. Only the points on the border make up the circle. The circle is only made up of the points on the border. Interior points are places within the hoop that are not part of the circle. The radius is the distance between the midpoint and the circle boundary. The diameter is a line segment that has the circle’s endpoints and passes through the midpoint. The radius is twice as large as the diameter. A chord can be defined as a line segment that has both ends on the circular boundary but does not pass through the middle.

The circumference of a circle is the distance covered by the boundary around the radius. The circumference of a circle can be calculated using the radius, r or diameter d. The formula is 

Circumference,c = 2 π r

c = π d

Types of points in a plane with a circle

On the plane of a circle, there are three types of points. They are the diameter of a circle’s exterior, interior, and point. Let us understand them briefly.

• Exterior points are points in the plane of the circle whose distance from the centre is larger than the radius ‘r’ of the circle. If OX > r, a point X is an exterior point in relation to a circle with the centre’ O’. In the above figure, we can observe points A, D and B are the exterior points.
• An interior-point is a point in the plane of a circle that is less than the radius of the circle. If OX < r, a point X is inside the circle with the centre’ O’. In the above figure, we can observe points F, D and B are the interior points.
• Points on the plane of the circle whose distance from its centre equal the radius of the circle are points on a circle’s circumference. A set of points lying on the circle are just points on the circle’s circumference. In the above diagram, we can observe points S, R and P are the interior points.

Different parts of a circle

Secant

It is the line that intersects the circle in the figure at two unique places. The secant of the circle is shown in the figure. Because its endpoints are on the circle’s perimeter, the line segment is known as the chord of the circle. The biggest chord of the circle is its diameter, and it passes through the centre of the circle.

Tangent

A line that touches the circle exactly at one point. The tangent to the circle is a line that touches the circle at a single point and stretches indefinitely.

Chord

A chord of the circle is a line segment that connects two places on the circumference of a circle. Any number of chords can be found in a circle. A circle’s diameter is its largest chord.

Segment

A segment of the circle is a portion of a circle circumscribed by a chord and an arc.

Arc 

An arc is a part or a portion of the circumference of a circle.

Sector

A circle’s sector is the area enclosed by two radii and a circle’s arc.

In this figure, an arc, sector, segment, secant, chord, tangent, diameter and radius is represented for better understanding. 

Conclusion

On the plane of a circle, there are three types of points. They are exterior, interior and points on the circumference of a circle whereas a circle can be defined as a collection of points in a plane that are all the same distance from the centre. The radius of a circle can be defined as the distance between its centre and a point on the circle. The diameter of the circle is the biggest chord of the circle, and it passes through the centre of the circle. In this article, we learnt about the points in the same plane with the circle and different parts of the circle.