IB Maths AA HL 3.1 Geometry and trigonometry - SL content Question Bank

1.
A circle of radius 4 cm , centre O , is cut by a chord $[\mathrm{AB}]$ of length 6 cm .

The logo, for a company that makes chocolate, is a sector of a circle of radius 2 cm , shown as shaded in the diagram. The area of the logo is $3 \pi \mathrm{~cm}^{2}$.

The points A and B lie on a circle, with centre O and radius 19.5 cm , such that $\mathrm{BO} \widehat{\mathrm{O}}=210^{\circ}$.
A piece of paper is cut into the shape of the sector BOA .
A hollow cone with no base is constructed from the sector by joining the points A and B . The sector forms the curved surface of the cone.
This is shown in the following diagrams.

Find

1.
The points P and Q lie on a circle, with centre O and radius 8 cm , such that $P \hat{\mathrm{O}} \mathrm{Q}=59^{\circ}$.

Find the area of the shaded segment of the circle contained between the $\operatorname{arc} \mathrm{PQ}$ and the chord [PQ].

The following diagram shows a regular pentagon inscribed in a circle with centre O and radius $r \mathrm{~cm}$.
The angle $\mathrm{A} \hat{\mathrm{O}} \mathrm{B}$ is $\theta$, where $\theta$ is measured in radians.
The $\operatorname{arc} \mathrm{AB}$ is 12 cm .

ABCD is a quadrilateral where AB=6.5, BC=9.1, CD=10.4, DA=7.8 and $\mathrm{C} \hat{\mathrm{D}} \mathrm{A}=90^{\circ}$. Find $\mathrm{A} \hat{\mathrm{B}} \mathrm{C}$, giving your answer correct to the nearest degree.

The cities Lucknow (L), Jaipur (J) and Delhi (D) are represented in the following diagram. Lucknow lies 500 km directly east of Jaipur, and JLD $=25^{\circ}$.

The bearing of D from J is $034^{\circ}$.

Given that $\frac{\pi}{2}<\alpha<\pi$ and $\cos \alpha=-\frac{3}{4}$, find the value of $\sin 2 \alpha$.

The following diagram shows a sector of a circle where $\mathrm{A} \hat{\mathrm{O}} \mathrm{B}=x$ radians and the length of the $\operatorname{arc} \mathrm{AB}=\frac{2}{x} \mathrm{~cm}$.
Given that the area of the sector is $16 \mathrm{~cm}^{2}$, find the length of the arc AB .