Ex 11.2, 7
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle
In this question, we need to find center of circle first.
As perpendicular to the chord passes through the center,
So, to find center,
We construct two non-parallel chords
And then, finding the point of intersection of their perpendicular bisectors.
Steps to draw center of circle
Draw a circle with the help of a bangle.
Draw two non parallel chords AB and CD
Draw perpendicular bisector of AB
Draw perpendicular bisector of CD
Where the two perpendicular bisectors intersect, mark it as center of circle O
Now, we need to draw tangents to this circle.
Steps of construction
Draw point P outside the circle
3. Join PO.
Make perpendicular bisector of PO
Let M be the midpoint of PO.
4. . Taking M as centre and MO as radius,
draw a circle.
5. Let it intersect the given circle at points Q and R.
6. Join PQ and PR.
∴ 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.
(Since Tangent is perpendicular
to radius)

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.