Question

The chord of a circle of radius 10 cm subtends a right angle at its center. Find (1) minor arc (2) major sector (3) minor segment.

a) (1) 60°, (2) 240°, (3) 50π cm²
b) (1) 90°, (2) 270°, (3) 25π cm²
c) (1) 45°, (2) 180°, (3) 100π cm²
d) (1) 30°, (2) 120°, (3) 75π cm²

Answer 1

The (1) minor arc is 20 cm, (2) major sector is 270°, and (3) minor segment is 25π cm².

Step-by-step explanation:

To find the (1) minor arc, (2) major sector, and (3) minor segment, we can use the relationship between angles and arc lengths in a circle. Since the chord subtends a right angle at the center, we know that the minor arc is equal to the sum of the two radii, which is 20 cm. The major sector is the entire circle except for the minor arc, so its measure is 360° - 90° = 270°. To find the area of the minor segment, we can use the formula: Area = (θ/360°) * π * r^2 - (1/2) * r^2 * sin(θ), where θ is the central angle of the segment. Since the chord subtends a right angle, θ is 90°. Plugging in the values, we get: Area = (90°/360°) * π * (10 cm)^2 - (1/2) * (10 cm)^2 * sin(90°) = (1/4) * π * 100 cm² = 25π cm².