0580/21 May/Jun 2022, Question 18: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 3 marks
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The question, in short
Using a circle with tangent TU at D, parallel chords DA and CB, and given angles 38° and 60°, find x and y.
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Solution · 3 marks
- 1x = angle UDC = 38 (alternate segment theorem)
- 2Angle ACB = angle DAC = 38 (alternate angles, DA parallel to CB)
- 3Angle ABC = 180 − 60 = 120 (opposite angles of a cyclic quadrilateral)
- 4y = 180 − 120 − 38 = 22 (angles in a triangle)
- 5x = 38, y = 22
Answerx = 38, y = 22
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Also searched as: 0580/21/M/J/22 · 0580_s22_qp_21 · 0580 s22 21 · question 18.
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