Skip to content

Form 4 Basic Properties of Circles Practice

Form 4 · 60 practice questions with instant marking and worked solutions.

Basic Properties of Circles is an important part of the Form 4 mathematics curriculum. This topic develops radius, diameter, circumference, area and angle properties. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.

A reliable approach to Basic Properties of Circles has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.

The 60 original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Basic Properties of Circles; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample. 8 of them are DSE Paper 1 style structured questions answered in parts (a), (b), (c), where later parts build on earlier ones.

Effective revision is more than recording a score. After completing the Basic Properties of Circles set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.

Basic Properties of Circles should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.

This batch adds 20 questions, bringing the topic to 60. The new questions cover controlled variations of different concepts, with paired bilingual conditions, hints, worked solutions and reproducible checks.

Start practising

  1. 1 Basic
    An angle at the circumference subtended by an arc is 25°. Find the angle at the centre. Choose the correct answer.
  2. 2 Basic
    An angle at the circumference subtended by an arc is 30°. Find the angle at the centre. Give the numerical value only.

  3. 3 Basic
    An angle at the circumference subtended by an arc is 35°. Find the angle at the centre. Show the essential working and give the numerical value.

    Reproducible diagram for Basic Properties of Circles; values and labels are stated in the question

  4. 4 Basic
    In Basic Properties of Circles, the value of $2\times 20^\circ$ is 41. Is this statement true?
  5. 5 Basic
    $A$, $B$ and $C$ lie on a circle with centre $O$, $C$ on the major arc, and $\angle ACB=52^\circ$. Find $\angle AOB$ in degrees. Choose the correct answer.
  6. 6 Basic
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=67^\circ$. Find $\angle ADC$ in degrees. Give the answer only.

  7. 7 Basic
    $AB$ is a diameter and $C$ lies on the circle with $\angle CAB=33^\circ$. Find $\angle CBA$ in degrees. Show the essential working and give the answer.

  8. 8 Basic
    A circle has radius 13 cm and chord $AB$ is 5 cm from the centre $O$. The length of $AB$ in cm is 12. Is this true?
  9. 9 Basic
    $A$, $B$ and $C$ lie on a circle with centre $O$, $C$ on the major arc, and $\angle ACB=64^\circ$. Find $\angle AOB$ in degrees. Choose the correct answer.
  10. 10 Basic
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=91^\circ$. Find $\angle ADC$ in degrees. Give the answer only.

  11. 11 Basic
    $AB$ is a diameter and $C$ lies on the circle with $\angle CAB=42^\circ$. Find $\angle CBA$ in degrees. Show the essential working and give the answer.

  12. 12 Basic
    A circle has radius 5 cm and chord $AB$ is 3 cm from the centre $O$. The length of $AB$ in cm is 4. Is this true?
  13. 13 Standard
    An angle at the circumference subtended by an arc is 30°. Find the angle at the centre. Choose the correct answer.
  14. 14 Standard
    An angle at the circumference subtended by an arc is 35°. Find the angle at the centre. Give the numerical value only.

  15. 15 Standard
    An angle at the circumference subtended by an arc is 40°. Find the angle at the centre. Show the essential working and give the numerical value.

  16. 16 Standard
    In Basic Properties of Circles, the value of $2\times 25^\circ$ is 50. Is this statement true?
  17. 17 Standard
    $P$ is 15 cm from the centre $O$; the radius is 9 cm and $PT$ is a tangent from $P$ touching at $T$. Find the length of $PT$ in cm. Choose the correct answer.
  18. 18 Standard
    $PA$ and $PB$ are tangents from an external point $P$ to a circle with centre $O$, and $\angle AOB=80^\circ$. Find $\angle APB$ in degrees. Give the answer only.

  19. 19 Standard
    $A$, $B$ and $C$ lie on a circle with centre $O$, $C$ on the major arc, and $\angle ACB=56^\circ$. Find $\angle AOB$ in degrees. Show the essential working and give the answer.

  20. 20 Standard DSE long question
    $AB$ is a chord of a circle with centre $O$ and radius 25 cm, and $O$ is 7 cm from $AB$. $M$ is the midpoint of $AB$. Answer each part; give the answer only.
    1. (a) Find $AM$ in cm.
    2. (b) Find $AB$ in cm.
    3. (c) Find the area of $\triangle OAB$ in cm².
    4. (d) Find the greatest distance from a point on the major arc to $AB$ in cm.
  21. 21 Standard
    $P$ is 13 cm from the centre $O$; the radius is 5 cm and $PT$ is a tangent from $P$ touching at $T$. Find the length of $PT$ in cm. Choose the correct answer.
  22. 22 Standard
    $PA$ and $PB$ are tangents from an external point $P$ to a circle with centre $O$, and $\angle AOB=96^\circ$. Find $\angle APB$ in degrees. Give the answer only.

  23. 23 Standard
    $A$, $B$ and $C$ lie on a circle with centre $O$, $C$ on the major arc, and $\angle ACB=28^\circ$. Find $\angle AOB$ in degrees. Show the essential working and give the answer.

  24. 24 Standard DSE long question
    $AB$ is a chord of a circle with centre $O$ and radius 17 cm, and $O$ is 8 cm from $AB$. $M$ is the midpoint of $AB$. Answer each part; give the answer only.
    1. (a) Find $AM$ in cm.
    2. (b) Find $AB$ in cm.
    3. (c) Find the area of $\triangle OAB$ in cm².
    4. (d) Find the greatest distance from a point on the major arc to $AB$ in cm.
  25. 25 Advanced
    An angle at the circumference subtended by an arc is 35°. Find the angle at the centre. Choose the correct answer.
  26. 26 Advanced
    An angle at the circumference subtended by an arc is 40°. Find the angle at the centre. Give the numerical value only.

  27. 27 Advanced
    An angle at the circumference subtended by an arc is 45°. Find the angle at the centre. Show the essential working and give the numerical value.

  28. 28 Advanced
    In Basic Properties of Circles, the value of $2\times 30^\circ$ is 61. Is this statement true?
  29. 29 Advanced
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=115^\circ$. Find $\angle ADC$ in degrees. Choose the correct answer.
  30. 30 Advanced
    $AB$ is a diameter and $C$ lies on the circle with $\angle CAB=21^\circ$. Find $\angle CBA$ in degrees. Give the answer only.

  31. 31 Advanced
    A circle has radius 5 cm and chord $AB$ is 3 cm from the centre $O$. The length of $AB$ in cm is 8. Is this true?
  32. 32 Advanced DSE long question
    $ABCD$ is a cyclic quadrilateral inscribed in a circle with centre $O$. $\angle ABC=68^\circ$, $\angle BAD=114^\circ$, and $E$ lies on $AD$ produced. Answer each part; give the answer only.
    1. (a) Find $\angle ADC$ in degrees.
    2. (b) Find $\angle BCD$ in degrees.
    3. (c) Find $\angle CDE$ in degrees.
    4. (d) Find the non-reflex angle $\angle AOC$ in degrees.
  33. 33 Advanced
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=79^\circ$. Find $\angle ADC$ in degrees. Choose the correct answer.
  34. 34 Advanced
    $AB$ is a diameter and $C$ lies on the circle with $\angle CAB=54^\circ$. Find $\angle CBA$ in degrees. Give the answer only.

  35. 35 Advanced
    A circle has radius 13 cm and chord $AB$ is 5 cm from the centre $O$. The length of $AB$ in cm is 24. Is this true?
  36. 36 Advanced DSE long question
    $ABCD$ is a cyclic quadrilateral inscribed in a circle with centre $O$. $\angle ABC=68^\circ$, $\angle BAD=66^\circ$, and $E$ lies on $AD$ produced. Answer each part; give the answer only.
    1. (a) Find $\angle ADC$ in degrees.
    2. (b) Find $\angle BCD$ in degrees.
    3. (c) Find $\angle CDE$ in degrees.
    4. (d) Find the non-reflex angle $\angle AOC$ in degrees.
  37. 37 Challenging
    An angle at the circumference subtended by an arc is 40°. Find the angle at the centre. Choose the correct answer.
  38. 38 Challenging
    An angle at the circumference subtended by an arc is 45°. Find the angle at the centre. Give the numerical value only.

  39. 39 Challenging
    An angle at the circumference subtended by an arc is 50°. Find the angle at the centre. Show the essential working and give the numerical value.

  40. 40 Challenging
    In Basic Properties of Circles, the value of $2\times 35^\circ$ is 70. Is this statement true?
  41. 41 Challenging
    $P$ is 5 cm from the centre $O$; the radius is 3 cm and $PT$ is a tangent from $P$ touching at $T$. Find the length of $PT$ in cm. Choose the correct answer.
  42. 42 Challenging
    $PA$ and $PB$ are tangents from an external point $P$ to a circle with centre $O$, and $\angle AOB=76^\circ$. Find $\angle APB$ in degrees. Show the essential working and give the answer.

  43. 43 Challenging
    $A$, $B$ and $C$ lie on a circle with centre $O$, $C$ on the major arc, and $\angle ACB=42^\circ$. $\angle AOB$ in degrees is 42. Is this true?
  44. 44 Challenging DSE long question
    $AB$ is a chord of a circle with centre $O$ and radius 13 cm, and $O$ is 5 cm from $AB$. $M$ is the midpoint of $AB$. Answer each part; give the answer only.
    1. (a) Find $AM$ in cm.
    2. (b) Find $AB$ in cm.
    3. (c) Find the area of $\triangle OAB$ in cm².
    4. (d) Find the greatest distance from a point on the major arc to $AB$ in cm.
  45. 45 Challenging
    $P$ is 20 cm from the centre $O$; the radius is 12 cm and $PT$ is a tangent from $P$ touching at $T$. Find the length of $PT$ in cm. Choose the correct answer.
  46. 46 Challenging
    $PA$ and $PB$ are tangents from an external point $P$ to a circle with centre $O$, and $\angle AOB=104^\circ$. Find $\angle APB$ in degrees. Show the essential working and give the answer.

  47. 47 Challenging
    $A$, $B$ and $C$ lie on a circle with centre $O$, $C$ on the major arc, and $\angle ACB=66^\circ$. $\angle AOB$ in degrees is 66. Is this true?
  48. 48 Challenging DSE long question
    $AB$ is a chord of a circle with centre $O$ and radius 10 cm, and $O$ is 6 cm from $AB$. $M$ is the midpoint of $AB$. Answer each part; give the answer only.
    1. (a) Find $AM$ in cm.
    2. (b) Find $AB$ in cm.
    3. (c) Find the area of $\triangle OAB$ in cm².
    4. (d) Find the greatest distance from a point on the major arc to $AB$ in cm.
  49. 49 Elite
    An angle at the circumference subtended by an arc is 45°. Find the angle at the centre. Choose the correct answer.
  50. 50 Elite
    An angle at the circumference subtended by an arc is 50°. Find the angle at the centre. Give the numerical value only.

  51. 51 Elite
    An angle at the circumference subtended by an arc is 55°. Find the angle at the centre. Show the essential working and give the numerical value.

  52. 52 Elite
    In Basic Properties of Circles, the value of $2\times 40^\circ$ is 81. Is this statement true?
  53. 53 Elite
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=55^\circ$. Find $\angle ADC$ in degrees. Give the answer only.

  54. 54 Elite
    $AB$ is a diameter and $C$ lies on the circle with $\angle CAB=60^\circ$. Find $\angle CBA$ in degrees. Show the essential working and give the answer.

  55. 55 Elite
    A circle has radius 29 cm and chord $AB$ is 20 cm from the centre $O$. The length of $AB$ in cm is 42. Is this true?
  56. 56 Elite DSE long question
    $ABCD$ is a cyclic quadrilateral inscribed in a circle with centre $O$. $\angle ABC=64^\circ$, $\angle BAD=82^\circ$, and $E$ lies on $AD$ produced. Answer each part; give the answer only.
    1. (a) Find $\angle ADC$ in degrees.
    2. (b) Find $\angle BCD$ in degrees.
    3. (c) Find $\angle CDE$ in degrees.
    4. (d) Find the non-reflex angle $\angle AOC$ in degrees.
  57. 57 Elite
    $ABCD$ is a cyclic quadrilateral with $\angle ABC=100^\circ$. Find $\angle ADC$ in degrees. Give the answer only.

  58. 58 Elite
    $AB$ is a diameter and $C$ lies on the circle with $\angle CAB=39^\circ$. Find $\angle CBA$ in degrees. Show the essential working and give the answer.

  59. 59 Elite
    A circle has radius 30 cm and chord $AB$ is 18 cm from the centre $O$. The length of $AB$ in cm is 48. Is this true?
  60. 60 Elite DSE long question
    $ABCD$ is a cyclic quadrilateral inscribed in a circle with centre $O$. $\angle ABC=70^\circ$, $\angle BAD=98^\circ$, and $E$ lies on $AD$ produced. Answer each part; give the answer only.
    1. (a) Find $\angle ADC$ in degrees.
    2. (b) Find $\angle BCD$ in degrees.
    3. (c) Find $\angle CDE$ in degrees.
    4. (d) Find the non-reflex angle $\angle AOC$ in degrees.

The report lists what you got wrong and why. Only you can see it.

Common mistakes

Common mistakes in Basic Properties of Circles

This topic needs particular care with radius, diameter, circumference, area and angle properties. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.

More Form 4 topics

Form 4 mixed revision → My mistakes →

Keep missing the same type?

Repeating the same mistake usually means an earlier concept never landed. We find that step in the trial lesson.

Book a Trial WhatsApp us
WhatsApp