Ex 11.2, 5
Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Steps of construction
Draw line segment AB of length 8 cm
Taking A as center, draw a circle of radius 4 cm
Taking B as center, draw a circle of radius 3 cm
Now, we need to draw tangent from point A to the right circle,
and from point B to the left circle.
To draw tangents to the right circle, we need to draw perpendicular bisector of line AB
4. Make perpendicular bisector of AB
Let M be the midpoint of AB.
5. Taking M as center and MA as radius,
draw a circle.
6. Let blue circle intersect left circle at P, Q
Let blue circle intersect right circle at R, S
Join BP, BQ, AR and AS
∴ AR, AS and BP, BQ are the required tangents
Justification
We need to prove that BP, BQ, AR, AS are the tangents to the circle.
Join OP, OQ, OR and OS
Now,
∠APB is an angle in the semi-circle of the blue circle
And we know that,
Angle in a semi-circle is a right angle.
∴ ∠ABP = 90°
⇒ AP ⊥ BP
Since AP is the radius of the circle,
BP has to be a tangent of the circle.
Similarly, we can prove
BQ, AR, AS are tangents 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.