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€™. 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.

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

- Draw a circle with required radius with center \(O\)
- Join center of the circle \(O\)
and any point P on the circle. \(OP\) is radius of the circle. - Draw a line perpendicular to radius \(OP\)
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.

How to draw two tangents from a point outside of the circle is discussed below.

Consider a point A outside the circle with center \(O\)

- Join the points A and O, bisect the line \(AO\)
. Let \(P\) be the midpoint of \(AO\) . - Draw a circle taking \(P\)
as center and \(PO\) as radius. This circle will intersect at two points \(B\) and \(C\) on the circle with center \(O\) . - Join point \(A\)
with \(B\) and \(C\) . \(AB\) and \(AC\) are the required tangents through points \(B\) and \(C\) on the circle.

Why \(AB\)

Join \(BO\)

It is observed that \(AO\)

Therefore,

\(âˆ ABO\)

Since, \(OB\)

Similarly, \(AC\)

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

- Draw two non-parallel chords \(AB\)
and \(CD\) . - Draw perpendicular bisector for both \(AB\)
and \(CD\) . - The point \(O\)
at which these bisectors intersect will be the center of the circle because, radius is perpendicular bisector to chord.

- Now, follow the steps to draw tangents when the center is given.

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