Question

The figure shows two concentric circles and AD is a chord of 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 - PB = PD - PC
⇒ AB = CD