Question

Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.

Answer 1

Steps of construction:

Step 1: Draw a line segment AB = 7 cm.

Step 2: With centre A and radius 3 cm, draw a circle.

Step 3: With centre B and radius 2 cm, draw a circle.

Step 4: Bisect the line AB. Let the mid-point of AB be C.

Step 5: Taking C as centre, draw a circle with AC as radius that intersect the circles at points P, Q, R and S.

Step 6: Join BP, BQ, AS and AR.

Here, BP, BQ, AS and AR are the tangents to each circle from the centre of the other circle.

Answer 2

Steps of construction:

1. Draw a line segment AB = 7 cm.
2. With A as centre and radius 3 cm draw a circle.
3. With B as centre and radius 2 cm draw another circle.
4. Taking AB as diameter draw another circle, which intersects first two circles at P and Q, R and S.
5. Join B to P, B to Q, A to R and A to S. 
   Hence, BP, BQ, AR and AS are the required tangents.