Construction of Tangents to a Circle

Let us study about construction of tangents to a circle,
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 you 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.
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.

Construction : To construct the tangents to a circle from a point outside it.
We are given a circle with centre 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 centre 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 (see Fig.).
Now let us see how this construction works.
Join OQ. Then ∠ PQO is an angle in the
semicircle and, therefore,
∠ PQO = 90°
Can we 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.
Note : If centre of the circle is not given, you may locate its centre first by taking any
two non-parallel chords and then finding the point of intersection of their perpendicular
bisectors. Then you could proceed as above.
Hope the above explanation helped you, now let me explain types of tangent lines.