The diagram shows a sector, $AOB,$ of a circle, centre $O,$ with radius $5 \mathrm{cm}$ and sector angle $\frac{\mathrm{\pi }}{3}$ radians. The lines $AP$ and $BP$ are tangents to the circle at $A$ and $B$, respectively. Find the exact area of the shaded region.

The diagram shows three touching circles with radii $6 \mathrm{cm}, 4 \mathrm{cm}$ and $2 \mathrm{cm}$.The area of the shaded region is $k {\mathrm{cm}}^2$, then find the value of $k$. [Write your answer in decimal only]

The diagram shows a semicircle, centre $O$, with radius $8 \mathrm{cm}$. $FH$ is the arc of a circle, centre $E$. Find the area of triangle $EOF$. [Answer up to three significant figures].

The diagram shows a semicircle, centre $O$, with radius $8 \mathrm{cm}$. $FH$ is the arc of a circle, centre $E$. Find the area of sector $FOG$.

The diagram shows a semicircle, centre $O$, with radius $8 \mathrm{cm}$. $FH$ is the arc of a circle, centre $E$. Find the area of sector $FEH$.

The diagram shows a semicircle, centre $O$, with radius $8 \mathrm{cm}$. $FH$ is the arc of a circle, centre $E$. Find the area of the shaded region.

The diagram shows a sector, $EOG$, of a circle, centre $O$, with radius $r \mathrm{cm}$. The line $GF$ is a tangent to the circle at $G$, and $E$ is the midpoint of $OF$. The perimeter of the shaded region is $p \mathrm{cm}$. Show that $P=\frac{r}{3}\left(3+3\sqrt{3}+\mathrm{\pi }\right)$

The diagram shows a sector, $EOG$, of a circle, centre $O$, with radius $r \mathrm{cm}$. The line $GF$ is a tangent to the circle at $G$, and $E$ is the midpoint of $OF$. The area of the shaded region is $A {\mathrm{cm}}^2$. Show that $A=\frac{r^2}{6}\left(3\sqrt{3}-\mathrm{\pi }\right)$.

The diagram shows two circles with radius $r \mathrm{cm}$. The centre of each circle lies on the circumference of the other circle. Find, in terms of $r$, the exact area of the shaded region.