In this blog, we will discuss how to construct a tangent to a circle. We have already learned that if a point lies inside a circle, there cannot be a tangent to the circle through this point. However, if a point lies on the circle, then there is only one tangent to the circle at this point and it is perpendicular to the radius through this point.

Therefore, if we want to draw a tangent at a point of a circle, simply draw the radius through this point and draw a line perpendicular to this radius through this point and this will be the required tangent at the point.

We have also seen that if the point lies outside the circle, there will be two tangents to the circle from this point. We shall now see how to draw these tangents.

What is Tangent to a Circle?

A circle's tangent is a line that intersects the circle exactly at one point. The point at which the tangent touches the circle is called the 'point of contact'. At the point of contact, the circle's radius and tangent are perpendicular to one another.

We know that no tangent to the circle can be made through a point within the circle. There can only be one tangent to a circle point.

Steps To Construct a Tangent to a Circle

Construction: To construct the tangents to a circle from a point outside it. We are given a circle with a center O and a point P outside it. We have to construct the two tangents from P to the circle.

Steps of Construction:

1. Join PO and bisect it. Let M be the midpoint of PO.

2. Taking M as center and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R. 3. Join PQ and PR. Then PQ and PR are the required two tangents.

Now let us see how this construction works.

Join OQ. Then ?PQO is an angle in the semicircle and, therefore, ?PQO = 90. So we can say that PQ?OQ. Since OQ is a radius of the given circle; PQ has to be a tangent to the circle. Similarly, PR is also a tangent to the circle.

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