Maharashtra Board Solutions for Exercise 3: Practice Set 17.2

The diameters $\mathrm{PQ}$ and $\mathrm{RS}$ of the circle with centre $\mathrm{C}$ are perpendicular to each other at $\mathrm{C}$. State, why arc $\mathrm{PS}$ and arc $\mathrm{SQ}$ are congruent. Write the other arcs which are congruent to arc $\mathrm{PS}$.

In the adjoining figure $\mathrm{O}$ is the centre of the circle whose diameter is $\mathrm{MN}$. Measures of some central angles are given in the figure. Hence, find the following:

$\left(i\right) m\angle AOB \text{and} m\angle COD$.

$\left(ii\right)$ Show that $\mathrm{arc} AB\cong \mathrm{arc} CD$.

$\left(iii\right)$ Show that $\mathrm{chord} \mathrm{AB}\cong \mathrm{chord} \mathrm{CD}$.