In a circle with centre P, chord AB ≅ chord CD and m∠APB = 40° Find the measure of ∠CPD

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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