The diagram shows a cord going around a pulley and a pin. The pulley is modelled as a circle with centre $$\(O\)$$ and radius $$\(5 \mathrm{~cm}\)$$. The thickness of the cord and the size of the pin $$\(P\)$$ can be neglected. The pin is situated $$\(13 \mathrm{~cm}\)$$ vertically below $$\(O\)$$. Points $$\(A\)$$ and $$\(B\)$$ are on the circumference of the circle such that $$\(A P\)$$ and $$\(B P\)$$ are tangents to the circle. The cord passes over the major arc $$\(A B\)$$ of the circle and under the pin such that the cord is taut. 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Exam No：9709_s20_qp_13 Year：2020 Question No：5
Answer:
\(\cos P O A=\frac{5}{13} \rightarrow P O A=1.17(6) \quad\) Allow \(67.4^{\circ}\)
or \(\sin =\frac{12}{13}\) or \(\tan =\frac{12}{5}\)
Reflex \(A O B=2 \pi-2 \times\) their \(1.17(6)\) OE in degrees or minor arc \(\mathrm{AB}=5 \times 2 \times\) their \(1.17(6)\)
Major arc \(=5 \times\) their 3.93(1) or \(2 \pi \times 5\) - their \(11.7(6)\)
\(A P(\) or \(B P)=\sqrt{13^{2}-5^{2}}=12\)
Cord length \(=43.7\)
or \(\sin =\frac{12}{13}\) or \(\tan =\frac{12}{5}\)
Reflex \(A O B=2 \pi-2 \times\) their \(1.17(6)\) OE in degrees or minor arc \(\mathrm{AB}=5 \times 2 \times\) their \(1.17(6)\)
Major arc \(=5 \times\) their 3.93(1) or \(2 \pi \times 5\) - their \(11.7(6)\)
\(A P(\) or \(B P)=\sqrt{13^{2}-5^{2}}=12\)
Cord length \(=43.7\)
Knowledge points:
1.4.2 use the formulae in solving problems concerning the arc length and sector area of a circle (Including calculation of lengths and angles in triangles and areas of triangles.)
Solution:
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