Question

The figure shows two concentric circles and AD is a chord of a larger circle.
Prove that: AB = CD.

Answer 1

Drop OP ⊥ AD
∴ OP bisects AD.     ....( Perpendicular drawn from the centre of a circle to a chord bisects it. )
⇒ AP = PD               .....(i)

Now, BC is a chord for the inner circle and OP ⊥ BC.
∴ OP bisects BC      ....( Perpendicular drawn from the centre of a circle to a chord bisects it. )
⇒ BP = PC               .....(ii)

Subtracting (ii) from (i),
AP - BP = PD - PC 
⇒ AB = CD.