Angle of Sector

Q.

Kim has a long pole of length 2m which makes an angle of ${20}^{\circ }$ with vertical. Kim takes a rope of length 5m and ties it to the pole. Now Kim moves along a circle so that the angle between initial and final rope positions is ${22}^{\circ }$. What is the radius and angle subtended by the arc formed by Kim’s movement?

1. 2 m , ${20}^{\circ }$.

2. 5 m , ${20}^{\circ }$

3. 2 m , ${20}^{\circ }$

4. 5 m, ${22}^{\circ }$

Q. In a circle whose radius is $10$ inches, a chord is $6$ inches from the center. What is the length of the chord?

1. $8$ inches
2. $6$ inches
3. $4$ inches
4. $16$ inches

Q.

From the figure shown, find $\angle$ APB in degrees, if $\angle$ AOB = ${120}^{\circ }$.

__

Q. A circular garden of radius 10m has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of 6 m from the centre of the garden. Find the angle subtended by the fence with the center of the garden. It is given that cos(${53}^{\circ }$) = $\frac{3}{5}$.

1. ${53}^{\circ }$
2. ${37}^{\circ }$
3. ${106}^{\circ }$
4. ${212}^{\circ }$