QQuestion
AB and CD are two chords of a circle. If we extend BA and DC, they intersect each other at point P. Prove that ∠PCB = ∠PAD.
✓Answer
Given, AB and CD are two chords of a circle
ABCD is a cyclic quadrilateral,
So, the opposite angles in a cyclic quadrilateral is equal to 180°
⇒ ∠BCD + ∠BAD = 180°
⇒ ∠BAD = 180° – ∠BCD
⇒ ∠BAD = 180° – ∠PCB — (i) [∵ ∠BCD = ∠PCB]
From the fig, ∠PAD + ∠BAD = 180° (Linear pair)
⇒ ∠PAD = 180° – ∠BAD
From the equation (i)
⇒ ∠PAD = 180° – (180° – ∠PCB)
∴ ∠PAD = ∠PCB (Proved)
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