Mathematics

Circle

Class X

Learning Points

1. Circle
2. Tangent to a Circle
3. Number of Tangents from a Point on a Circle

Circle

Circle is a collection of points. These points are located at a certain distance from a fixed point. The fixed point is known as centre. The certain distance is known as radius. A circle has centre, radius, diameter, circumference, Tangent, secant, chord. These are basic terminology of a circle.

Any lines which passing through one and only one point of circle is said to be tangent. Any lines which join two point of a circle is said to be secant. Any lines which passing through a circle without touching it is said to be non - intersectiong line.

Tangent to a Circle

Any lines which passing through one and only one point of circle is said to be tangent. Tangent is a Latin word derived from tangere means touching.

There is one and only one tangent at certain point of a circle. 

Tangent is a special types of secant in which two ends point coincides. Therefor all tangents are secant but all secant are not a tangent.

Theorem 10.1

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Given:-

There is a circle. O is the centre. P is a point on the circle. The tangent XY passing through P.

To Prove that :-

XY is perpendicular on OP.

Construction:-

Point Q is on XY outside of the circle. Join OQ.

Proof:

OQ is greater than OP.

If Q lies inside the circle.

XY will be secant.

OP is the shortest distance from centre O.

We know that the shortest distance from a point on line is perpendicular.

Therefore,

XY is perpendicular on OP. Proved.

1. By theorem above, we can also conclude that at any point on a circle there can be one and only one tangent.

2. The line containing the radius through the point of contact is also sometimes called the ‘normal’ to the circle at the point.

In next part I shall post "Number of Tangents from a Point on a Circle". Please do wait for this.