O Level / IGCSE Mathematics chapter 4: Geometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

72 exam-style questions on Geometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

72 questions · 8 topics · 10 per test

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What chapter 4 covers

Ten Geometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A net consists of one square with a congruent isosceles triangle attached to each of its four sides. Which solid does it fold to make?

  1. A
    cube
  2. B
    tetrahedron
  3. C
    triangular prism
  4. D
    square-based pyramid
Show answer

Answer: D. The square is the base and the four triangles fold up to meet at the apex: a square-based pyramid. A tetrahedron has four triangular faces and no square.

2. A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the perpendicular distance from the centre to the chord.

  1. A
    12.8 cm
  2. B
    6 cm
  3. C
    8 cm
  4. D
    2 cm
Show answer

Answer: B. The perpendicular from the centre bisects the chord, making a right-angled triangle with hypotenuse 10 and side 8. Distance = √(102 − 82) = √36 = 6 cm.

3. An angle measures 215°. What type of angle is it?

  1. A
    reflex
  2. B
    right
  3. C
    acute
  4. D
    obtuse
Show answer

Answer: A. A reflex angle is between 180° and 360°, so 215° is reflex. An obtuse angle is between 90° and 180°.

4. To bisect a line AB of length 10 cm, arcs of equal radius are drawn centred at A and at B on both sides of AB. Which radius would NOT give crossing points?

  1. A
    7 cm
  2. B
    9 cm
  3. C
    4 cm
  4. D
    6 cm
Show answer

Answer: C. The arcs only meet if the radius is more than half of AB, which is 5 cm. With 4 cm the arcs do not reach each other.

5. A, B and C lie on a circle with centre O, and C is on the major arc AB. Angle OAB = 25°. Find angle ACB.

  1. A
    50°
  2. B
    130°
  3. C
    25°
  4. D
    65°
Show answer

Answer: D. OA = OB (radii), so angle OBA = 25° and angle AOB = 180° − 50° = 130°. The angle at the circumference is half the angle at the centre: 65°.

6. A vertical pole 2 m tall casts a shadow 3.2 m long. At the same time a tree casts a shadow 20 m long. How tall is the tree?

  1. A
    18.8 m
  2. B
    32 m
  3. C
    12.5 m
  4. D
    6.4 m
Show answer

Answer: C. The two right-angled triangles are similar. Height ÷ shadow is the same: tree height = 20 × 2 ÷ 3.2 = 12.5 m. Using 3.2 ÷ 2 instead gives 32.

7. How many lines of symmetry does a rhombus (that is not a square) have?

  1. A
    2
  2. B
    0
  3. C
    1
  4. D
    4
Show answer

Answer: A. A rhombus has 2 lines of symmetry: its two diagonals. The lines through the midpoints of opposite sides are not lines of symmetry unless it is a square, which has 4.

8. Each interior angle of a regular polygon is 5 times each exterior angle. How many sides does the polygon have?

  1. A
    6
  2. B
    12
  3. C
    5
  4. D
    30
Show answer

Answer: B. Interior + exterior = 180°, so 5e + e = 180 and e = 30°. Number of sides = 360 ÷ 30 = 12. 30 is the exterior angle, not the number of sides.

9. What is the order of rotational symmetry of a regular hexagon?

  1. A
    2
  2. B
    3
  3. C
    6
  4. D
    12
Show answer

Answer: C. A regular hexagon fits onto itself 6 times in a full turn (every 60°), so the order is 6. It also has 6 lines of symmetry.

10. Which set of lengths cannot be used to construct a triangle?

  1. A
    5 cm, 6 cm, 10 cm
  2. B
    2 cm, 3 cm, 6 cm
  3. C
    3 cm, 4 cm, 5 cm
  4. D
    4 cm, 4 cm, 7 cm
Show answer

Answer: B. The two shorter sides must add to more than the longest side. 2 + 3 = 5, which is less than 6, so the arcs would never meet. In the others 7, 8 and 11 are all greater than the longest side.

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Ways to practise this chapter

Geometry: questions students ask

How many Geometry MCQs are there?

72, each with the answer and a short explanation, across 8 topics: Geometrical terms, Geometrical constructions, Scale drawings, Similarity, Symmetry, Angles, Circle theorems I, Circle theorems II. Every chapter test draws ten of them, so you can take it many times.

Is the O Level / IGCSE Mathematics chapter 4 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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