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