Problems adapted from questions set for previous Mathematics exams.
The points B, C, D, E and F are on a circle. DAE and CAB are straight lines and AB= BE.
Calculate the value of \(x\).
B, C, D and E are points on the circumference of a circle, centre O.
BD is a diameter of the circle and the diagram is not drawn to scale.
(a) Find the size of angle DBE and give a reason for your answer.
(b) Find the size of angle DBC and give a reason for your answer.
In the diagram above, not drawn to scale, A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line. AC is a diameter and angle OTA = 28°.
(a) angle AOT
(b) angle ACB
(c) angle ABT
(a) Find \(x\), the size of angle ABC if B, C and D are all points on the circle to which AB is a tangent. The diagram is not drawn to scale.
(b) Give a reason for your answer
The diagram, not drawn to scale, shows chords joining points on the circumference of a circle. Prove that triangle ADE is similar to triangle BCE.
The diagrams are not drawn to scale
ABCDEF is a hexagon with AB parallel to ED and BC parallel to FE.
GFE and GABH are straight lines. Angle CBH = 70o and angle EFA = 90o.
Calculate the values of:
K, P, J and N are points on a circle and KN = NP.
KJ is a diameter and LKM is the tangent to the circle at K.
Angle LKN = 59o.
Find the values of: