Question

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. 

Answer 1

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.