AB is a diameter of a circle, and C is a point on the circumference (not at A or B). What is the size of angle ACB?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Circle theorems Topical Past Papers.
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These Circle theorems Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Geometry (E4.7) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Apply circle theorems: angle in a semicircle, angle at centre = twice angle at circumference, angles in the same segment, opposite angles in a cyclic quadrilateral, tangent-radius (perpendicular at point of contact), tangents from an external point.
AB is a diameter of a circle, and C is a point on the circumference (not at A or B). What is the size of angle ACB?
Two points A and B lie on a circle with centre O. The angle AOB at the centre is 100°. Find the size of the angle ACB at the circumference, subtended by the same arc AB.
[1 mark]ABCD is a cyclic quadrilateral. Angle BAD = 75°. Find the size of angle BCD.
[2 marks]Points P, Q, R and S lie on a circle in that order, with P and R on the same side of chord QS. Angle QPS = 38°. Find the size of angle QRS.
[2 marks]A tangent to a circle meets the radius drawn to the point of contact. What is the angle between the tangent and the radius?
A and B are two points on a circle with centre O. Angle AOB at the centre is 80°. C is a point on the major arc AB (the longer arc) and D is a point on the minor arc AB.
Find the size of angle ACB.
[1 mark]Find the size of angle ADB.
[2 marks]Two tangents from an external point P touch a circle (centre O) at points A and B. Angle APB = 50°. Find the size of angle AOB.
[2 marks]Triangle ABC is inscribed in a circle, where AB is a diameter. Angle CAB = 35°. Find the size of angle ABC.
[2 marks]