Angles in a semicircle, same segment, centre, tangent.
12 original questions, 44 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
A, B, C and D are points on a circle, in that order round the circumference, so ABCD is a cyclic quadrilateral.
Angle DAB = 108° and angle ABC = 75°.
Give a reason for each answer.
A, B, C and D are points on a circle, in that order round the circumference. The chords AC and BD cross at X.
Angle ABD = 34° and angle CAB = 52°.
Give a reason for each answer.
A, B and C are points on a circle with centre O.
AOC is a diameter of the circle.
Angle CAB = 37°.
Work out the size of angle ACB. Give a reason for each stage of your working.
A, B and C are points on a circle with centre O.
B lies on the major arc AC.
Angle AOC = 128°.
Work out the size of angle ABC. Give a reason for your answer.
A, B and C are points on a circle. The line PAQ is the tangent to the circle at A. B and C are on the same side of PQ, with B nearer to P.
Angle PAB = 64° and angle BAC = 50°.
Give a reason for each stage of your working.
A and B are points on a circle with centre O.
TA and TB are tangents to the circle from the point T.
Angle ATB = 48°.
Work out the size of angle AOB. Give a reason for each stage of your working.
TP is a tangent to a circle with centre O. P is the point where the tangent touches the circle. Angle POT = 58°.
A, B, C and D are points on a circle, in that order.
Angle ABD = 29° and angle DBC = 46°.
Work out the size of
Give a reason for each stage of your working.
A, B and C are points on a circle with centre O.
C lies on the major arc AB.
Angle OAB = 28°.
Work out the size of angle ACB. Give a reason for each stage of your working.
A and C are points on a circle with centre O.
PC is a tangent to the circle at C.
Angle PCA = 58°.
Work out the size of angle OAC. Give a reason for each stage of your working.
A, B and C are points on a circle with centre O.
B lies on the minor arc AC.
Angle AOC = 114°.
Work out the size of
Give a reason for each stage of your working.
AB is a diameter of a circle with centre O. C is a point on the circle. The tangent to the circle at C meets AB extended beyond B at the point T.
Angle CAB = 25°.
Give a reason for each stage of your working.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.