A polygon has 54 diagonals. The number of sides in the polygon is:

In the given figure, two circles with their respective centres intersect each other at $\mathrm{A}$ and $\mathrm{B}$ and $\mathrm{AB}$ intersects $\mathrm{OO}\text{'}$ at $\mathrm{M}$, then $\angle \mathrm{OMA}$ is :

In the given figure, two circles with their respective centres intersect each other at $\mathrm{A}$ and $\mathrm{B}$ and $\mathrm{AB}$ intersects $\mathrm{OO}\text{'}$ at $\mathrm{M}$, then what is the ratio of $\mathrm{AM}:\mathrm{BM}$?

In the adjoining figure, $\mathrm{O}$ is the centre of the circle and diameter $\mathrm{AC}=26 \mathrm{cm}$. If chord  $\mathrm{AB}=10 \mathrm{cm}$, then the distance between chord $\mathrm{AB}$ and centre $\mathrm{O}$ of the circle is:

In the adjoining circle $\mathrm{C}(0,\mathrm{r})$ the degree measure of minor arc $\mathrm{AB}=130°$. Find the degree measure of major arc.

If the diagonals of cyclic quadrilateral are equal, then the quadrilateral is