(a)[2]
Find the value of $x$. Give a reason to support your answer.
(b)[2]
Find the value of $y$. Give a reason to support your answer.
Mathematics 0580 · IGCSE · Circle theorems I
Circle theorems I — practice question
The diagram represents a circle with centre $O$ and diameter $AC$. The points $A, B, C, D$ and $E$ are all on the circle's circumference. This sketch is not drawn to scale. At $C$, the angle between $CB$ and $CO$ is $65^\circ$. At $D$, the angle between $DO$ and $DE$ is $46^\circ$. At $A$, the angle between $AO$ and $AB$ is labelled $x^\circ$. At $E$, the angle between $EO$ and $EA$ is labelled $y^\circ$.