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.

Calculate the size of the lettered angle in the diagram.

Calculate the size of the lettered angle in the diagram.

Calculate the value of $x$ in the diagram.

Calculate the value of $x$ in the diagram.

In the diagram, $BCF$ and $BAE$ are the tangents to the circle at $C$ and $A$ respectively. $AD$ is a diameter and angle $ABC=40°$. Explain why triangle $ABC$ is isosceles.