5 \includegraphics[max width=\textwidth, alt={}, center]{aa4c496d-ce5f-4f46-ad37-d901644a9e7c-06_761_460_258_840} 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 cm . The thickness of the cord and the size of the pin \(P\) can be neglected. The pin is situated 13 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. Calculate the length of the cord.

## Question 5:

$\cos POA = \frac{5}{13} \rightarrow POA = 1.17(6)$, allow $67.4°$; or $\sin = \frac{12}{13}$ or $\tan = \frac{12}{5}$ | M1 A1 |

Reflex $AOB = 2\pi - 2 \times their\ 1.17(6)$, OE in degrees; or minor arc $AB = 5 \times 2 \times their\ 1.17(6)$ | M1 |

Major arc $= 5 \times their\ 3.93(1)$; or $2\pi \times 5 - their\ 11.7(6)$ | M1 |

$AP$ (or $BP$) $= \sqrt{13^2 - 5^2} = 12$ | B1 |

Cord length $= 43.7$ | A1 |

---

5\\
\includegraphics[max width=\textwidth, alt={}, center]{aa4c496d-ce5f-4f46-ad37-d901644a9e7c-06_761_460_258_840}

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 cm . The thickness of the cord and the size of the pin $P$ can be neglected. The pin is situated 13 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.

Calculate the length of the cord.\\

\hfill \mbox{\textit{CAIE P1 2020 Q5 [6]}}