0580/23 May/Jun 2024, Question 14: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 3 marks
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The question, in short
Circle with tangent AB at T and points P, Q, R, T on it; angle ATP = 50°, angle PTR = 48°, PQ = QR. Find angle PRT and angle QPR.
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Part (a) · 1 mark
Find angle PRT using the tangent-chord angle ATP = 50°.
- 1Alternate segment theorem: angle PRT = angle ATP
- 2Angle PRT = 50°
Answer50
Part (b) · 2 marks
Find angle QPR, using angle PTR = 48° and PQ = QR.
- 1PQRT is cyclic, so angle PQR = 180 − 48 = 132°
- 2Triangle PQR is isosceles (PQ = QR)
- 3Angle QPR = (180 − 132) ÷ 2 = 24°
Answer24
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Also searched as: 0580/23/M/J/24 · 0580_s24_qp_23 · 0580 s24 23 · question 14.
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