Question

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verily the measurement by actual calculation.

Answer 1

Steps of Construction : 

1. With ‘O’ as centre two circles are constructed with radii 4 cm and 6 cm. 

2. Draw OM radius for small circle and drawn perpendicular at M which meets big circle at P and Q. 

3. Now PQ is the tangnet drawn for small circle.

Tangent PMQ = 9 cm 

Verification : In ⊥∆OMP, ∠M = 90°. 

∴ OM² + PM² = OP² 

(4)² + PM² = (6)² 

PM² = (6)² – (4)² = 36 – 16 

PM² = 20 

∴ PM = √20 = 4.5 cm. 

Similarly, MQ = 4.5 cm. 

∴ PQ = PM + MQ = 4.5 + 4.5 

∴ PQ = 9 cm.