Question 1: Calculate the length of the segment's minor arc when the central angle is 60° in a circle with radius 10 cm.

Answer: 10.47 cm

Question 2: Find the area of the segment formed by a chord that cuts off a 90° sector in a circle of radius 12 cm.

Answer: 37.7 cm²

Question 3: A circle has a radius of 15 cm. A segment is formed by a chord that creates a 45° central angle. Calculate the height of this segment.

Answer: 5.89 cm

Question 4: Construct a circle with a radius of 8 cm and draw a segment corresponding to a 120° central angle. Measure and record the length of the arc.

Answer: 16.76 cm

Question 5: A chord divides a circle into two segments. If the segment's area is 20 cm² and the circle has a radius of 7 cm, find the measure of the central angle of the segment.

Answer: Approximately 55°

Question 6: Find the length of a chord that subtends a 30° arc in a circle with radius 9 cm.

Answer: 4.72 cm

Question 7: Identify and correct the mistake: A student states that the area of a segment with a 60° central angle in a circle of radius 10 cm is 78.5 cm².

Answer: Incorrect; the correct area is approximately 14.6 cm²

Question 8: Calculate the area of the segment formed by a 75° sector in a circle with radius 14 cm.

Answer: 28.4 cm²

Question 9: A segment in a circle is formed by a chord that creates a 50° central angle. The radius of the circle is 20 cm. Find the length of the segment's chord.

Answer: 16.5 cm

Question 10: A circle has a radius of 10 cm. A segment's area is found to be 15 cm². Determine whether the segment corresponds to a central angle greater than or less than 30°, and justify your answer.

Answer: Less than 30° because the segment area is smaller than the sector for 30°

Question 11: Compute the length of the arc corresponding to a 135° central angle in a circle with radius 9 cm.

Answer: 21.2 cm