Karen Morrison and Nick Hamshaw Solutions for Exercise 6: Exercise 19.6

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.

In the diagram, $BCF$ and $BAE$ are the tangents to the circle at $C$ and $A$ respectively. $AD$ is a diameter and angle $ABC=40°$. Calculate the value of $\angle CAB$.

In the diagram, $BCF$ and $BAE$ are the tangents to the circle at $C$ and $A$ respectively. $AD$ is a diameter and angle $ABC=40°$. Calculate the value of $\angle DAC$.

In the diagram, $BCF$ and $BAE$ are the tangents to the circle at $C$ and $A$ respectively. $AD$ is a diameter and angle $ABC=40°$. If $\angle ADC=k°$, then find the value of $k$.