7 \includegraphics[max width=\textwidth, alt={}, center]{01b98496-a717-4c68-8489-42d2203b700f-08_574_689_260_726} The diagram shows a sector \(A O B\) which is part of a circle with centre \(O\) and radius 6 cm and with angle \(A O B = 0.8\) radians. The point \(C\) on \(O B\) is such that \(A C\) is perpendicular to \(O B\). The arc \(C D\) is part of a circle with centre \(O\), where \(D\) lies on \(O A\). Find the area of the shaded region.

## Question 7:

| $OC = 6\cos 0.8 = 4.18(0)$ | M1A1 | SOI |
|---|---|---|
| Area sector $OCD = \frac{1}{2}(\text{their}\,4.18)^2 \times 0.8$ | \*M1 | OE |
| $\triangle OCA = \frac{1}{2}\times 6 \times \text{their}\,4.18\times\sin 0.8$ | M1 | OE |
| Required area $= \text{their}\,\triangle OCA - \text{their sector}\,OCD$ | DM1 | SOI. If not seen *their* areas of sector and triangle must be seen |
| 2.01 | A1 | CWO. Allow or better e.g. 2.0064 |
| **Total: 6** | | |

---

7\\
\includegraphics[max width=\textwidth, alt={}, center]{01b98496-a717-4c68-8489-42d2203b700f-08_574_689_260_726}

The diagram shows a sector $A O B$ which is part of a circle with centre $O$ and radius 6 cm and with angle $A O B = 0.8$ radians. The point $C$ on $O B$ is such that $A C$ is perpendicular to $O B$. The arc $C D$ is part of a circle with centre $O$, where $D$ lies on $O A$.

Find the area of the shaded region.\\

\hfill \mbox{\textit{CAIE P1 2020 Q7 [6]}}