Q. 234.5( 2 Votes )

# In the figure, P is a point on the chord BC such that AB = AP. Prove that, CP = CQ.

Answer :

Given P is a point on the chord BC and AB = AP

.

∠ABP = ∠AQC ..............(ii)[angle in the same segment of a circle] and

∠APB = ∠CPQ...............(iii) [Vertically opposite angles]

.

⇒ CQ = PC

or CP = CQ

.

^{.}. ∠ABP = ∠APB ...........(i)∠ABP = ∠AQC ..............(ii)[angle in the same segment of a circle] and

∠APB = ∠CPQ...............(iii) [Vertically opposite angles]

.

^{.}. ∠CPQ = ∠ AQC = ∠PQC [from (i)]⇒ CQ = PC

or CP = CQ

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