In a circle, the perpendicular bisector of a chord must pass through the centre of the circle.

Consider the following statements in respect of any triangle.

$\mathrm{I}$. The three medians of a triangle divide it into six triangles of equal area.

$\mathrm{II}$. The perimeter of a triangle is greater than the sum of the lengths of its three medians.

In the given figure, $\mathrm{ABCD}$ is a square in which $\mathrm{AO}=\mathrm{AX}$. What is $\angle \mathrm{XOB}$?

In the given figure, $\mathrm{AB}$ is a diameter of a circle and $\mathrm{CD}$ is perpendicular to $\mathrm{AB}$. If $\mathrm{AB}=10 \mathrm{cm}$ and $\mathrm{AE}=2 \mathrm{cm}$, then what is the length of $\mathrm{ED}$?

In the given figure, $\mathrm{AD}$ is a straight line. $\mathrm{OP}\perp \mathrm{AD}$ and $\mathrm{O}$ is the centre of both circles. If $\mathrm{OA}=20 \mathrm{cm}$, $\mathrm{OB}=15 \mathrm{cm}$ and $\mathrm{OP}=12 \mathrm{cm}$, what is $\mathrm{AB}$ equal to?