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

Answer 1

PQ perpendicular to RS.
$$\begin{gathered} \angle \mathrm{PCS}=\angle \mathrm{PCQ}=90° \\ \Rightarrow \mathrm{arc}\left(\mathrm{PS}\right)=\mathrm{arc}\left(\mathrm{QS}\right) \end{gathered}$$
We know that if the measures of two arcs of circle are same then two arcs are congruent
$\Rightarrow \mathrm{arc}\left(\mathrm{PS}\right)\cong \mathrm{arc}\left(\mathrm{QS}\right)$
Similarly,
$\Rightarrow \mathrm{arc}\left(\mathrm{PS}\right)\cong \mathrm{arc}\left(\mathrm{PR}\right)\cong \mathrm{arc}\left(\mathrm{RQ}\right)$