Unit 6

In the diagram, O is the centre of the circle. AB is a tangent to the circle at A. OC is a diameter. OA and OB are radii, and angle OAB = 28°.

ABCD is a cyclic quadrilateral. Angle ABC = 76°, angle CDA = 88°. Work out the size of angle BAD.

In a circle, the chord AB is 8 cm long and is perpendicular to the radius at its midpoint. If the radius of the circle is 5 cm, work out the perpendicular distance from the centre of the circle to the chord, giving your answer to 2 decimal places.

In the diagram, OA and OB are radii of the circle, centre O. TB is a tangent to the circle at point B. Angle OBA = 68°.

AB and CD are two chords of a circle, intersecting at point P inside the circle. AP = 3 cm, PB = 6 cm, CP = 4 cm.

State the alternate segment theorem and give an example of how it can be used to find an unknown angle in a circle.

A tangent touches a circle at point T. The chord AB passes through T. Given that angle ATB = 37°, write down the size of the angle in the alternate segment which is subtended by AB, and state which theorem you used.

In the diagram, O is the centre of the circle. QR and ST are two chords which intersect at right angles at point P inside the circle. If OP = 3 cm, QR = 6 cm, and ST = 8 cm, find the radius of the circle.

Explain how the alternate segment theorem can be used to find an unknown angle in a circle. Give a clear step-by-step example, including both the reasoning and the calculation.

List the members of the set {prime numbers less than 15}.