A circle is defined as a set of all points in a plane which are equally spaced from a fixed point. The fixed point is called the centre of the circle and the distance between any point on the circle and its centre is called the radius of the circle.
Based on the positions and their properties a circle has different parts. The important parts of a circle are explained below in detail. Arc - It is basically the connected curve of a circle. Sector - A region bounded by two radii and an arc. Points to remember that segments do not contain the centre. Centre - Midpoint of a circle is known as the centre.
Chord - It is a line segment that joins two points on the circle. Endpoints of the chord lie on the circle. Diameter - It is a line segment having both the endpoints on the circle and is the largest chord of the circle.
Radius - It is the line segment connecting the centre of a circle to any point on the circle itself. Secant - It is a straight line which cuts the circle at two points. It is also known as an extended chord. Tangent - It is a straight line touching the circle at a single point. A line segment connecting the centre of a circle to any point on the circle itself is known as the radius of the circle.
The radius is denoted by R or r. Diameter is defined as the longest chord of the circle. It is twice the length of radius i. The radius of the circle can be derived from the diameter of the circle. All the important point related to the circle are shown below in the diagram. The important basic properties of the circle are as follows:. The outer line of a circle which is circumference is at equidistant from the centre. The diameter of the circle divides the circle into two equal parts.
Two circles are said to be congruent to each other if they have equal radii. Circles which are different in size or have different radii are known as similar circles. The diameter is the largest chord of the circle and is double the radius. A tangent to a circle is a line which touches the circle exactly at one point. For every point on the circle, There is a unique tangent for every point on the circle passing through it.
The tangent to the circle at any point is the perpendicular to the radius of the circle that passes through the point of contact.
The length of the tangent to the circle is defined as the segment of the tangent from the external point P to the point of tangency I with the circle. In the given diagram below, PI is the length of a tangent. Two tangents of equal length can be drawn from an external point of a circle. The space occupied by the shape circle is known as an area of the circle. The area of a circle is given by the formula below. The circumference of a circle is the length of the line around the edges of the circle.
Circumference of a circle is calculated by multiplying pi with 2 times radius. Mathematically can be expressed as.
Equal chord of a circle subtends an equal angle at the centre. The perpendicular to a chord bisects the chord if the line drawn from the centre of the circle.
Equal chords of a circle are equidistant i. The measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the centre by the same arc.
In a cyclic quadrilateral, the opposite angles are supplementary.
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