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4024/23 May/Jun 2025, Question 17: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 23 (Calculator) · Calculator · 5 marks

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The question, in short

Circle with points B, D, E, F; tangent AC at B; angle BEF = 50° and EF = BF. Find x and y with geometrical reasons.

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Part (a) · 2 marks

Find x, the angle between BF and BC, giving a geometrical reason.

  1. 1x = angle BEF = 50
  2. 2Alternate segment theorem

Answer50, alternate segment theorem

Part (b) · 3 marks

Find y, angle EDB, giving a geometrical reason for each step.

  1. 1EF = BF, so angle FBE = angle BEF = 50° (isosceles triangle)
  2. 2Angle EFB = 180 − 50 − 50 = 80° (angles in a triangle)
  3. 3y = 180 − 80 = 100 (opposite angles of a cyclic quadrilateral add to 180°)

Answer100, isosceles triangle, opposite angles of a cyclic quadrilateral sum to 180°

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Also searched as: 4024/23/M/J/25 · 4024_s25_qp_23 · 4024 s25 23 · question 17.
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