Question

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Answer 1

Radius of big circle, 

OA = OB = 5 cm. 

Radius of small circle, OP = 3 cm. 

Angle between radius and tangent is 90°. 

∴ ∠OPA = ∠OPB = 90° 

( ∵ Chord AB is tangent to small circle.) 

Now, in ⊥∆ OPA, ∠OPA = 90° 

OP² + AP² = OA² 

(3)² + AP² = (5)² 

9 + AP² = 25 

∴ AP² = 25 – 9 

AP² = 16 

∴ AP = 4 cm. 

Similarly, in ⊥∆OPB, PB = 4 cm. 

∴ Length of chord, AB = AP + PB = 4 + 4 

∴ Chord, AB = 8 cm.