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The Chords Corresponding to Congruent Arcs Are Congruent

In a circle w...

Question

In a circle with centre O, the chord PQ ≅ chord AB and m∠AOB = 70°. Find the measure of ∠POQ.

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Solution

In the given circle, chord PQ ≅ chord AB and m $∠$ AOB = 70°.
m $∠$ AOB ≅ m $∠$ POQ = 70° (Congruent chords of the same circle form congruent angles at the centre of the circle)

∴ m $∠$ POQ = 70°

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