Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Given, two concentric circles of radii 3 cm and 5 cm with centre O. We have to draw pair of tangents from point P on outer circle to the other.

Steps of construction:

1. Draw two concentric circles with centre O and radii 3cm and 5cm.

2. Taking any point P on outer circle. Join OP.

3. Bisect OP, let M’ be the mid-point of OP.

To bisect OP:

a. With P as centre and any radius more than half of the length of OP, draw two arcs on either side of OP.

b. Similarly, with O as centre and any radius more than half of the length of OP; draw two arcs on either side of OP which intersect with the previous arcs at M and N.

c. Join MN to meet the line OP at M’, which is the mid-point.

4. Taking M’ as centre and OM’ as radius draw a circle dotted which cuts the inner circle at A and B.

5. Join PA and PB. Thus, PA and PB are required tangents.

6. On measuring PA and PB, we find that PA=PB=4 cm.

Actual calculation:

In the right angle ∆OAP,

∠PAO=90°

According to Pythagoras theorem

(hypotenuse)²=(base)² + (perpendicular)²

PA²=(5)²-(3)²=25-9=16

PA=4 cm

Hence, the length of both tangents is 4 cm.

Therefore, PA = PB = 4cm