4024/12 Oct/Nov 2020, Question 23: Combining Circle Theorems
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Two touching circles with centres O and Q, line ORT tangent to the larger circle at T; given OR = 4 cm, RT = 6 cm and larger radius x cm, find x.
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Solution · 4 marks
- 1OP = OR = 4 and PQ = QT = x, so OQ = 4 + x and OT = 4 + 6 = 10
- 2Tangent is perpendicular to radius, so angle OTQ = 90°: OQ² = OT² + TQ²
- 3(x + 4)² = 10² + x²
- 4x² + 8x + 16 = 100 + x²
- 58x = 84, so x = 10.5
Answer10.5
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