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

If the diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral,prove that it is a rectangle.

In the given figure,if $\angle BCD = 40^{\circ}$ and $\angle BAE = 65^{\circ},$ then find the values of $a, b,$ $c$ and $d$.

If a pair of opposite sides of a cyclic quadrilateral are equal,prove that its diagonals are also equal.

In an isosceles triangle $ABC$ with $AB = AC$,a circle passing through $B$ and $C$ intersects the sides $AB$ and $AC$ at $X$ and $Y$ respectively. Prove that $XY \parallel BC$.

In the figure,$\angle ADC = 130^{\circ}$ and chord $BC = $ chord $BE$. Find $\angle CBE$.