0580/23 May/Jun 2026, Question 15: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 3 marks
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The question, in short
Cyclic quadrilateral ABCD with diagonals AC and BD; angle ADB = 41° and angle ABC = 86°. Find angle ACB and angle BDC.
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Part (a) · 1 mark
Find angle ACB using the given angles in the cyclic quadrilateral.
- 1Angle ACB = angle ADB (angles in the same segment)
- 2Angle ACB = 41°
Answer41
Part (b) · 2 marks
Find angle BDC using the given angles in the cyclic quadrilateral.
- 1In triangle ABC: angle BAC = 180 − 86 − 41 = 53°
- 2Angle BDC = angle BAC (angles in the same segment)
- 3Angle BDC = 53°
Answer53
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Also searched as: 0580/23/M/J/26 · 0580_s26_qp_23 · 0580 s26 23 · question 15.
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