Ab and Cd Are Two Equal Chords of a Drde Intersecting at Pas Shown in Fig. Pis Joined to 0, the Centre of the Cirde. Prove that Op Bisects Lcpb. - Mathematics

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Sum

AB and CD are two equal chords of a drde intersecting at Pas shown in fig. P is joined to O , the centre of the cirde. Prove that OP bisects  ∠ CPB. 

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Solution

Draw perpendiculars OR and OS to CD and AB respectively. 

In triangle ORP and triangle OSP 

OP= OP 

OR = OS     (Distance of equal chords from centre are equal) 

∠ PRO = ∠ PSO (right angles) 

Therefore, Δ ORP  ≅  Δ OSP 

Hence, ∠ RPO = ∠ SPO 

Thus OP bisects ∠ CPB. 

  Is there an error in this question or solution?
Chapter 17: Circles - Exercise 17.1

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Frank ICSE Class 10 Mathematics Part 2
Chapter 17 Circles
Exercise 17.1 | Q 2

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