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Sum

The diameters PQ and RS of the circle with centre C are perpendicular to each other at C. state, why arc PS and arc SQ are congruent. Write the other arcs which are congruent to arc PS.

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#### Solution

PQ perpendicular to RS.

∠PCS = ∠SCQ = 90°

⇒ arc (PS) = arc (QS)

We know that if the measures of two arcs of circle are same then two arcs are congruent.

⇒ arc (PS) ≅ arc (QS)

Similarly,

⇒ arc (PS) ≅ arc (PR) ≅ arc (RQ)

Concept: Arcs Corresponding to the Chord of a Circle

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