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CAIE IGCSE Mathematics Circle Angle Theorems and Reasons

Practise choosing and naming the correct circle theorem to calculate unknown angles involving chords, diameters, radii and tangents.

Syllabus
2028–2030
Course
Mathematics 0580
Level
Extended

Exam points

  • use angle at centre = 2 × angle at circumference or equal angles in the same segment
  • use 90° in a semicircle, tangent perpendicular to radius or opposite cyclic angles summing to 180°
  • apply the alternate segment theorem and state it explicitly when linking a tangent to a chord angle

E4.7.1 Calculate unknown angles and give explanations using the following question 1

[Maximum number: 3]

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

[ 3 ]

Question (i)

(i)

angle AOC

[ 1 ]

Question (ii)

(ii)

angle ACO

 Angle ACO=\text { Angle } A C O=
[ 1 ]

Question (iii)

(iii)

angle ACD.

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