Question

How many tangents can be drawn at any point on the circle?
A) 0
B) 1
C) 2
D) 3

Answer 1

Hint:
Here, we have to find the number of tangents drawn on the circle. A tangent on the circle is a line that touches the circle at only one point. The tangent to the circle is always perpendicular to the radius of the circle at the tangential point.

Complete step by step solution:
First we will draw the circle with a tangent.
Let O be the centre of the circle and P be any point on the circle with centre O.
Let OP be the radius of the circle.
We will consider a line m passing through the point P on the circle and the point Q.

We have OP and PQ perpendicular to each other , so we know that the perpendicular distance is the shortest distance.
So, OP is the shortest distance since it is perpendicular to the line m.
The point P on the circle alone lies on the line m. The other points on the circle do not lie on the line m. Thus, the line m is a tangential line.
Therefore, the tangent line meets the circle at only one point.
So, we can say that only one tangent can be drawn at any point on the circle.

Thus Option(B) is correct.

Note:
We know that the point where the tangent touches the circle is called the point of contact. The length of the tangent from the external point is equal. The angle between the tangent and the chord is equal to the angle opposite to the chord. The tangent is a line which lies outside the circle whereas the chord is a line which lies inside the circle.