Geometry Circles & Arcs 2 — Questions and Answers
Question 1: A central angle measures 72°. What fraction of the full circle does its arc represent?
- 1/5 (Correct answer)
- 1/4
- 1/3
- 2/5
Correct answer: 1/5
72° ÷ 360° = 1/5 of the circle.
Question 2: An inscribed angle intercepts an arc of 100°. What is the measure of the inscribed angle?
- 50° (Correct answer)
- 100°
- 200°
- 80°
Correct answer: 50°
An inscribed angle is half its intercepted arc, so 100° ÷ 2 = 50°.
Question 3: A circle has radius 6. What is the length of an arc subtended by a central angle of 60°?
- 2π (Correct answer)
- 6π
- π
- 12π
Correct answer: 2π
Arc length = (60/360) × 2π(6) = (1/6)(12π) = 2π.
Question 4: Two tangents drawn from an external point to a circle are always:
- Equal in length (Correct answer)
- Perpendicular to each other
- Parallel
- Diameters
Correct answer: Equal in length
Tangent segments from a common external point are congruent.
Question 5: A sector has a central angle of 90° in a circle of radius 4. What is its area?
- 4π (Correct answer)
- 16π
- π
- 8π
Correct answer: 4π
Sector area = (90/360) × π(4²) = (1/4)(16π) = 4π.
Question 6: An angle inscribed in a semicircle always measures:
- 90° (Correct answer)
- 45°
- 180°
- 60°
Correct answer: 90°
An angle inscribed in a semicircle intercepts a 180° arc, so it is 90°.
Question 7: The measure of an arc equals the measure of its central angle. If an arc is 145°, its central angle is:
- 145° (Correct answer)
- 72.5°
- 290°
- 35°
Correct answer: 145°
A central angle has the same measure as the arc it intercepts.
Geometry Circles & Arcs 2
A central angle measures 72°.
What fraction of the full circle does its arc represent?