$P$ is a point inside a circle whose centre is $O$. Describe how to construct the chord that has $P$ as its mid-point.

A straight line cuts two concentric circles at $A, B, C, D$. Prove that $AB=CD$.

Apply what you have learned about circle properties to calculate the diameter of circle, if $AB=CD=11.4 \mathrm{cm}, OF=6.5 \mathrm{cm}$. Give approximate answer to $3$ significant figures.

Apply what you have learned about circle properties to calculate the diameter of circle, if $AB=2.8 \mathrm{cm}$. Give approximate answers to $3$ significant figures.

A circle with a radius of $8.4 \mathrm{cm}$ has a chord $5 \mathrm{cm}$ from its centre. Calculate the length of the chord (in $\mathrm{cm}$) correct to $2$ decimal places.

ln this diagram, find the length of $AO$ and the area of quadrilateral $AOCB$. $BA$ and $BC$ are tangents to the circle.

In the diagram, $AB$ and $AD$ are tangents to the circle. $ABC$ is a straight line. Calculate the size of angle $x$.

Calculate the size of the lettered angles in the diagram.

Calculate the size of the lettered angles in the diagram.