In the figure,if $\angle DAB = 60^{\circ}$ and $\angle ABD = 50^{\circ}$,then $\angle ACB$ is equal to: (in $^{\circ}$)

In the figure,$\angle ACB = 40^{\circ}$. Find $\angle OAB$.

If two equal chords of a circle intersect,prove that the parts of one chord are separately equal to the parts of the other chord.

If non-parallel sides of a trapezium are equal,prove that it is cyclic.

If arcs $AXB$ and $CYD$ of a circle are congruent,find the ratio of $AB$ and $CD.$

Prove that the angle bisector of any angle of a triangle and the perpendicular bisector of the opposite side,if they intersect,will intersect on the circumcircle of the triangle.