Construction 11.3 : 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 mid- point 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. 11.5).

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.