If centre of the circle is not given, (Ex 11.2, 7)
We find its center first by
- Taking any two non-parallel chords
- And then finding the point of intersection of their perpendicular bisectors.
Then you could proceed as 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 :
- Join PO and bisect it. Let M be the midpoint of PO.
- Taking M as centre and MO as radius, draw a circle.
- Let it intersect the given circle at the points Q and R.
- Join PQ and PR.
Then, PQ and PR are the required two tangents.
We need to prove that PQ and PR are the tangents to the circle.
Join OQ and OR.
∠PQO is an angle in the semi-circle
of the blue circle
And we know that angle in a
semi-circle is a right angle.
∴ ∠PQO = 90°
⇒ OQ ⊥ PQ
Since OQ is the radius of the circle,
PQ has to be a tangent of the circle.
Similarly, PR is a tangent of the circle.