Circle theorems and constructionsIB MYP Maths Extended: Mind map

Exam questions on Circle theorems and constructions

1. $A$, $B$ and $C$ are points on the circumference of a circle with centre $O$. $C$ is on the major arc $AB$ and angle $AOB=116^\circ$.
   $D$ is a point on the minor arc $AB$. Find the size of angle $ADB$, giving a reason.2 marks
2. $PQ$ is a diameter of a circle with centre $O$. $R$ is a point on the circle and angle $RPQ=35^\circ$. The line $QT$ is the tangent to the circle at $Q$, and $T$ is on the same side of $PQ$ as $R$.
   Find the size of angle $RQT$, giving a reason for each step.2 marks
3. Two tangents $TA$ and $TB$ are drawn from a point $T$ outside a circle with centre $O$. They touch the circle at $A$ and $B$. Angle $ATB=50^\circ$.
   Find the size of angle $TAB$. Give a reason for each step.3 marks