CAIE IGCSE Mathematics Extended Circle Theorem Questions

Practise calculating and justifying circle angles using semicircles, centre angles, same segments, cyclic quadrilaterals and tangents.

Syllabus
2028–2030
Topic
E4.7
Level
Extended

Exam points

  • identify the relevant chord, diameter, radius or tangent before selecting a circle theorem
  • calculate the angle and state the exact theorem, such as same segment or cyclic quadrilateral
  • combine alternate-segment or tangent–radius facts with triangle and straight-line angle sums

Covered syllabus points

E4.7.1 Calculate unknown angles and give explanations using the following

E4.7 Circle theorems I question 1

[Maximum number: 2]

NOT TO SCALE

A, B and C are points on the circle, centre O.
DE is a tangent to the circle at C.
AC=10 cm, AB=9.5 cm and BC=7.7 cm.

Question (a)

(a)

Find

[ 2 ]

Question (i)

(i)

angle AOC

[ 1 ]

Question (ii)

(ii)

angle ACD.

 Angle ACD=\text { Angle } A C D=
[ 1 ]
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