5th Form Christmas Term Assignment #2

P, Q, R and S are four points on the circumference of the circle shown. The angle at R is 58°. Determine the size of the angle at P.

• 122° (Reason: Opposing Angles in a Cyclic Quadrilateral are supplementary)

• 58° (Reason: Opposing Angles in a Cyclic Quadrilateral are equal)

• 58° (Reason: Angles in the alternate segments are equal)

• 122° (Reason: Angle at the centre is twice the angle at the circumference)

P, Q, R and S are four points on the circumference of the circle shown. The angle at R is 58°. Determine the size of the angle QOS.

• 32° (Reason: The angle at the centre and the angle at the circumference are complementary)

• 58° (Reason: The angle at the centre is equal to the angle at the circumference)

• 116° (Reason: The angle at the centre is twice the angle at the circumference)

• 116° (Reason: Angles in the same segment are equal)

P, Q, R and S are four points on the circumference of the circle shown. The angle at R is 58°. Determine the size of the OQS.

• 116° (Reason: Angle at the centre is twice the angle at the circumference)

• 122° (Reason: Angles in the same segment are supplementary)

• 58° (Reason: Angles in the same segment are equal)

The diagram, not drawn to scale, shows a circle, centre O. EH and EF are tangents to the circle. FOG and JOH are straight lines. The angle at E is 44°. Find the size of the angle EHF.

• 44° (Reason: Base angles in an isosceles triangle are equal)

• 136° (Reason: Angles in a triangle are supplementary)

• 46° (Reason: Angles in a triangle are complementary)

The diagram, not drawn to scale, shows a circle, centre O. EH and EF are tangents to the circle. FOG and JOH are straight lines. The angle at E is 44°. Find the size of the angle JHE.

• 90° (Reason: Perpendicular lines/right angles are formed where the radius of a circle meets the tangent of that circle)

• 46° (Reason: Adjacent angles in a quadrilateral are complementary)

• 68° (Reason: Angles in a triangle are supplementary)

• 68° (Reason: Base angles in an isosceles triangle are equal)

The diagram, not drawn to scale, shows a circle, centre O. EH and EF are tangents to the circle. FOG and JOH are straight lines. Find the size of the angle JGH.

• 46° (Reason: angles in the alternate segment are complementary)

• 90° (Reason: The angle in a semicircle is a right angle)

• 180° (Reason: opposite angles in a cyclic quadrilateral are supplementary)

• 44° (Reason: angles in the alternate segment are equal)