In the same plane,two circles can have a maximum of ............ common chords.

$O$ is the circumcentre of the triangle $ABC$ and $D$ is the mid-point of the base $BC$. Prove that $\angle BOD = \angle A$.

Three girls Reshma,Salma and Mandip are playing a game by standing on a circle of radius $5 \, m$ drawn in a park. Reshma throws a ball to Salma,Salma to Mandip,Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is $6 \, m$ each,what is the distance between Reshma and Mandip?

The region between an arc and the two radii,joining the centre to the end points of the arc is called a ........... .

The longest chord of a circle is a .......... of the circle.

In the figure,$\angle OAB = 30^{\circ}$ and $\angle OCB = 57^{\circ}$. Find $\angle BOC$ and $\angle AOC$.