#### Question

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.

#### Solution

PQ perpendicular to RS.

∠PCS = ∠PCQ = 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)

Is there an error in this question or solution?

Solution The Diameters Pq and Rs of the Circle with Centre C Are Perpendicular to Each Other at C. Concept: Arcs Corresponding to the Chord of a Circle.