Construction 11.3
To construct the tangents to a circle from a point outside it.
We are given a circle with center O
and point P outside the circle
We need to draw tangents from point P to the circle
Let’s follow these steps
Steps of construction
Join PO.
Make perpendicular bisector of PO
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 points Q and R.
Join PQ and PR.
Then, PQ and PR are the required two tangents.
Justification
We need to prove that PQ and PR are the tangents to the circle.
Join OQ and OR.
Now,
∠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.

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.