Q. 34.5( 2 Votes )

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

Answer :

Given: chord AB ≅ chord CD

AB = CD

m∠APB = 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, m∠APB = m∠CPD = 40° (By CPCT)

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Fill in the blanks.

In the circle with centre O shown alongside,

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