Geometry Circles & Arcs 3 — Questions and Answers
Question 1: A chord is 8 units long and is 3 units from the center. What is the radius (to nearest whole)?
- 5 (Correct answer)
- 4
- 6
- 7
Correct answer: 5
Half-chord 4, distance 3: r = √(4² + 3²) = √25 = 5.
Question 2: Two chords intersect inside a circle. One is divided into segments 3 and 8; the other into 4 and x. Find x.
- 6 (Correct answer)
- 5
- 7
- 12
Correct answer: 6
By the intersecting chords rule, 3×8 = 4×x, so x = 24/4 = 6.
Question 3: The circumference of a circle is 31.4. Using π ≈ 3.14, what is the diameter?
- 10 (Correct answer)
- 5
- 20
- 15
Correct answer: 10
C = πd, so d = 31.4 / 3.14 = 10.
Question 4: A tangent line meets a radius at the point of tangency at an angle of:
- 90° (Correct answer)
- 45°
- 60°
- 180°
Correct answer: 90°
A radius is always perpendicular to a tangent at the point of contact.
Question 5: The arc opposite a 40° inscribed angle measures:
- 80° (Correct answer)
- 40°
- 20°
- 160°
Correct answer: 80°
The intercepted arc is twice the inscribed angle: 2 × 40° = 80°.
Question 6: In a circle of radius 10, a sector has area 25π. What is its central angle?
- 90° (Correct answer)
- 45°
- 180°
- 120°
Correct answer: 90°
25π = (θ/360)π(100), so θ/360 = 1/4, giving θ = 90°.
Question 7: The longest chord in any circle is called the:
- Diameter (Correct answer)
- Radius
- Tangent
- Secant
Correct answer: Diameter
The diameter passes through the center and is the longest chord.
Geometry Circles & Arcs 3
A chord is 8 units long and is 3 units from the center.
What is the radius (to nearest whole)?