Question 1: Calculate the area of a segment of a circle with radius 10 cm, where the central angle subtending the segment is 60°.

Answer: ~8.73 cm^2

Question 2: A circle has radius 15 cm. The length of the chord that creates a segment with a 45° central angle is required. Calculate the length of the chord.

Answer: ~9.77 cm

Question 3: Determine the height (distance from the centre to the chord) of a segment with a 90° central angle in a circle of radius 12 cm.

Answer: ~8.49 cm

Question 4: In a circle of radius 8 cm, the segment subtends a 120° central angle. Find the area of the segment.

Answer: ~8.26 cm^2

Question 5: Construct a circle with radius 6 cm and draw a segment corresponding to a 75° central angle. Label all relevant parts.

Answer: Students draw the diagram with radius 6 cm, central angle 75°, and label the segment, chord, and radius.

Question 6: A segment of a circle with radius 20 cm has a chord length of 16 cm. Calculate the measure of the central angle that subtends this segment.

Answer: ~53.13°

Question 7: A circle with radius 9 cm has a segment whose area is 12.57 cm^2. Find the measure of the central angle of this segment.

Answer: ~50°

Question 8: A segment in a circle is formed by a 100° central angle. If the radius of the circle is 14 cm, find the length of the chord forming the segment.

Answer: ~19.3 cm

Question 9: A diagram shows a circle with radius 10 cm and a segment with a 30° central angle. The segment's height from the centre to the chord is 4.33 cm. Identify and explain the common mistake students might make when calculating the segment's area.

Answer: Mistake: Using the full sector area instead of subtracting the triangular area. Explanation: Segment area is sector minus triangle, not sector alone.

Question 10: A circle's radius is 18 cm. A segment subtends a central angle of 80°. Calculate the area of the segment. Then, determine the segment's height from the centre to the chord.

Answer: Segment area: ~23.65 cm^2; Height: ~8.49 cm

Question 11: Challenge: In a circle with radius 25 cm, find the maximum possible area of a segment that can be formed, and state the corresponding central angle.

Answer: Maximum segment area ~490.87 cm^2, central angle 180°.