Q. 34.5( 2 Votes )

In a circle with centre P, chord AB chord CD and mAPB = 40° Find the measure of CPD

Answer :

Given: chord AB chord CD

AB = CD


mAPB = 40°


We have a circle with centre P, Let us now draw a figure with the given information.



Join, PC and PD, we get,



Now, In ∆APB and ∆PCD


AB = CD (since, chordAB chord CD )


BP = PD (since, BP and PD are radius of a circle)


AP = PC (since, AP and PC are radius of a circle)


Thus, ∆APB∆PCD (By, SSS Congruent Rule)


Thus, mAPB = mCPD = 40° (By CPCT)


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