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.
The tangents can be constructed on the given circles as follows.
- Draw a line segment AB of 8 cm. Taking A and B as centre, draw two circles of 4 cm and 3 cm radius.
- Bisect the line AB. Let the mid-point of AB be C.
- Taking C as centre, AC as radius, draw a circle which intersects the circles at points P, Q, R, and S.
- Join BP, BQ, AS, and AR.
These are the required tangents.
We need to prove
- BP and BQ are tangents to larger circle.
- AS and AR are tangents to smaller circle.
- Join BS and BR.
∠ASB is an angle in the semi-circle of the blue circle
And we know that angle in a semi-circle is a right angle.
∴ ∠ASB = 90°
⇒ AS ⊥ BS
Since BS is the radius of the circle,
AS has to be a tangent of the circle.
Similarly, AR, BP, BQ are tangents.