#### Question

The figure shows two concentric circles and AD is a chord of larger circle.

Prove that: AB = CD

#### Solution

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

Is there an error in this question or solution?

Solution The Figure Shows Two Concentric Circles and Ad is a Chord of Larger Circle.Prove That: Ab = Cd Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof).