In cyclic quadrilateral $ABCD$,if $5 \angle A = 13 \angle C$,then find $\angle A$. (in $^{\circ}$)

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

Prove that if the angles subtended by the chords of a circle (or of congruent circles) at the centre (or the corresponding centres) are equal,then the chords are equal.

$A$ piece of a circle between two points on a circle is called ........ of the circle.

If $ABC$ is an equilateral triangle inscribed in a circle and $P$ is any point on the minor arc $BC$ which does not coincide with $B$ or $C$,prove that $PA$ is the angle bisector of $\angle BPC$.

Write True or False and justify your answer in each of the following: Through three collinear points a circle can be drawn.