0580/42 May/Jun 2025, Question 18: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 4 marks
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The question, in short
Using a circle through A, B, C, D and E with intersecting chords EB and AC, work out the sizes of angles x, y and z from the given 125°, 26° and 52°.
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Solution · 4 marks
- 1In the triangle formed by E, C and the crossing point: x = 180 − 125 − 26 = 29
- 2y = angle AEB = angle ACB = 52 (angles in the same segment)
- 3Angle EBC = 180 − 29 − (26 + 52) = 73 (angles in triangle EBC)
- 4z = 180 − 73 = 107 (opposite angles of cyclic quadrilateral EBCD)
- 5x = 29, y = 52, z = 107
Answerx = 29, y = 52, z = 107
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