Circle Theorems Practice Questions

Write down the mathematical name of the straight line $AB$.

The shaded region is bounded by the straight line $AB$ and the arc $AB$.

Write down the mathematical name of this shaded region.

Write down the mathematical name of the straight line $LDM$.

Work out the size of angle $ACB$.
Give a reason for your answer.

Work out the size of angle $OAB$.

$A$, $B$, $C$ and $D$ are points on the circumference of a circle.
$AC$ is a diameter of the circle.
Angle $BAC = 37^\circ$.

Diagram not accurately drawn

Work out the size of angle $ADB$.
You must give a reason for each stage of your working.

Show that $x = 30$.

Work out the size of angle $ABC$.

Work out the size of angle $TAB$.

$C$ is a point on the major arc $AB$.

Work out the size of angle $ACB$.
You must give a reason for each stage of your working.

Work out the radius of the circle.
You must give a reason for your first step of working.

$CD$ is a different chord of the same circle.
$CD = 12$ cm.

Work out the distance of the chord $CD$ from the centre of the circle.

Work out the size of angle $BAC$.

Work out the size of angle $ABC$ and the size of angle $ACB$.
You must give a reason for your answers.

$A$, $B$, $C$ and $D$ are points on the circumference of a circle, centre $O$.

Diagram not accurately drawn

Prove that angle $DAB$ + angle $BCD = 180^\circ$.

You may use the fact that the angle at the centre of a circle is twice the angle at the circumference.
You must give reasons for each stage of your working.

Prove that triangle $TAB$ and triangle $TCA$ are similar.
You must give reasons for each stage of your working.

$TB = 4$ cm and $BC = 5$ cm.

Work out the length of $TA$.

$A$, $B$ and $C$ are points on a circle, centre $O$.
$AOB$ is a diameter of the circle.
$CT$ is the tangent to the circle at $C$.
$AOBT$ is a straight line.
Angle $CAB = x^\circ$.

Diagram not accurately drawn

Prove that angle $ATC = (90 - 2x)^\circ$.
You must give a reason for each stage of your working.