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# Construction of Tangent to a Circle

In Geometry, a tangent is a line that touches the curve exactly at a point. The point is called the point of tangency. The tangent to a circle is defined as the perpendicular to the radius at the point of tangency. In this article, we are going to discuss what is tangent to a circle, how to construct a tangent to a circle, and also we will learn how to draw a tangent from the point outside of the circle with a step by step procedure.

## What is Tangent to a Circle?

Tangent of a circle is a line which touches the circle exactly at one point. The point at which tangent touches the circle is known as â€˜point of contactâ€™. The radius of the circle and tangent are perpendicular to each other at the point of contact.

We know that, there cannot be any tangent drawn to the circle through a point inside the circle.

There can be only one tangent to a point on the circle.

## Construction of Tangents to a Circle

Letâ€™s see how to draw a tangent to a circle at a point on the circle. (Refer fig.)

Step 1: Draw a circle with the required radius with centreÂ O

Step 2: Join centre of the circleÂ OÂ and any point P on the circle. OPÂ is the radius of the circle

Step 3: Draw a line perpendicular to radius OPÂ through point P. This line will be a tangent to the circle at P

Two tangents can be drawn to a circle from a point outside of the circle. Lengths of the two tangents will be equal.

## Construction of Two Tangents from a Point Outside of the Circle

Step 1:Consider a point A from the outside the circle with centreÂ O.

Step 2: Join points A and O, bisect the lineÂ AO. LetÂ PÂ be the midpoint ofÂ AO.

Step 3: Draw a circle takingÂ PÂ as centre andÂ POÂ as a radius. This circle will intersect at two pointsÂ BÂ andÂ CÂ on the circle with centreÂ O.

Step 4: Join the pointÂ AÂ withÂ BÂ andÂ C.Â ABÂ andÂ ACÂ are the required tangents through pointsÂ BÂ andÂ CÂ on the circle.

### WhyÂ ABÂ andÂ ACÂ are Tangents to the Circle with CentreÂ O?

Join BO. It is observed thatÂ AOÂ is a diameter of the circle with centreÂ P. By construction,Â âˆ ABOÂ is an angle in a semi-circle.

Therefore,

âˆ ABOÂ =Â 90Â°

SinceÂ OBÂ is the radius of the circle with centreÂ O,Â ABÂ has to the tangent through the pointÂ B.

Similarly,Â ACÂ is the tangent through the pointÂ C.

Note:

When the centre of the circle is not given to draw a tangent to the circle from a point outside the circle (Refer fig),

• Draw two non-parallel chordsÂ ABÂ andÂ CD.
• Draw perpendicular bisector for bothÂ ABÂ andÂ CD.
• The pointÂ OÂ at which these bisectors intersect will be the centre of the circle because the radius is perpendicular bisector to chord.

• Now, follow the steps to draw tangents when the centre is given.