Worksheet Chapter 5: Circles

1. In a circle with centre O, arc AB subtends an angle of 140° at O. Point C lies on the major arc AB. Calculate ∠ACB.

2. A chord of length 24 cm is drawn in a circle of radius 15 cm. Find the perpendicular distance from the centre of the circle to the chord.

3. Diagram shows a circle with centre O and radius 10 cm. A chord AB has a length of 12 cm. (a) Find the perpendicular distance from O to AB. (b) Calculate the angle ∠AOB in degrees and minutes. (c) Find the area of the minor segment bounded by chord AB.

4. Fill in the blank: The region bounded by two radii and an arc of a circle is called a ________.

5. Find the area of the shaded region if a sector with central angle 60° is cut out from a circle of radius 14 cm. (Take π = 227)

6. True or False: The angle subtended by an arc at the centre of a circle is equal to the angle subtended by the same arc at the circumference.

7. Which of the following represents the area of a sector with radius r and central angle θ?

8. True or False: The opposite interior angles of a cyclic quadrilateral are supplementary (add up to 180°).

9. A bicycle wheel has a diameter of 70 cm. (a) Calculate the distance traveled in meters when the wheel makes 500 complete rotations. (b) If the bicycle travels a total distance of 3.3 km, calculate the number of complete rotations made by the wheel. (Take π = 227)

10. Calculate the circumference of a circle with a radius of 10.5 cm. (Take π = 227)