Question

construct the tangents to a circle of radius4 cm from a point or the concentric circle of radius 6cm and measure its length also verify the measurements by actual calculations ​

Answer 1

1.Draw two concentric circles C1 and C2 with common Centre O and radius 4 cm 6 cm.

2. Take any point P on outer circle C2 and join OP.

3. Draw the bisector of OP which bisect OP at M’.

4. Taking M’ as centre and OM’ as radius draw a dotted circle with cuts the inner circle C1 at two points M & P’.

5.Join PM & PP’ . Thus PM & PP’ are Required tangents.

On measuring PM & PP’,

PM = PP’ = 4.4 cm

By calculation:

In ∆ OMP, ∠PMO= 90°

PM² = OP²  - OM²

[ by Pythagoras theorem]

PM² = (6)² -(4)²

= 36 - 16 = 20

PM² = 20 cm

PM = √20 = 4.4 cm

Hence, the length of the tangents is 4.4 cm.

HOPE THIS WILL HELP YOU.....