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1. The center of a circle lies in the ________ of the circle.
A. Exterior
B. Interior
C. Boundary
D. None of these
Answer: B. Interior
Explanation: The center of a circle always lies inside (interior) the circle.
2. A point whose distance from the center of a circle is greater than its radius lies in the ________ of the circle.
A. Interior
B. Exterior
C. On the circle
D. At the center
Answer: B. Exterior
Explanation: Distance > radius means the point is outside (exterior) the circle.
3. The longest chord of a circle is its:
A. Radius
B. Diameter
C. Secant
D. Tangent
Answer: B. Diameter
Explanation: The diameter is the longest chord that passes through the center of the circle.
4. An arc is a ________ when its ends are the ends of a diameter.
A. Major arc
B. Minor arc
C. Semicircle
D. Full circle
Answer: C. Semicircle
Explanation: An arc whose endpoints lie on the diameter is half a circle, known as a semicircle.
5. Segment of a circle is the region between an arc and the ________ of the circle.
A. Radius
B. Chord
C. Center
D. Tangent
Answer: B. Chord
Explanation: A circular segment is bounded by a chord and the corresponding arc.
6. A circle divides the plane on which it lies into ________ parts.
A. Two
B. Three
C. Four
D. Infinite
Answer: B. Three
Explanation: The three parts are: the interior, the circle itself, and the exterior.
7. The perpendicular from the center of a circle to a chord ________ the chord.
A. Trisects
B. Bisects
C. Quadruples
D. Does not affect
Answer: B. Bisects
Explanation: Theorem 10.3 states that a line drawn from the center perpendicular to a chord bisects the chord into two equal parts.
8. Equal chords of a circle subtend ________ angles at the center.
A. Right
B. Equal
C. Complementary
D. Supplementary
Answer: B. Equal
Explanation: Theorem 10.1 states that equal chords of a circle subtend equal angles at the center.
9. How many circles can pass through three non-collinear points?
A. Zero
B. Exactly one
C. Two
D. Infinitely many
Answer: B. Exactly one
Explanation: Theorem 10.5 states that there is one and only one circle passing through three given non-collinear points.
10. The angle subtended by an arc at the center is ________ the angle subtended by it at any point on the remaining part of the circle.
A. Equal to
B. Half of
C. Double
D. Triple
Answer: C. Double
Explanation: Theorem 10.8 states that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining circumference.
11. Angle subtended in a semicircle is a/an:
A. Acute angle
B. Right angle
C. Obtuse angle
D. Straight angle
Answer: B. Right angle
Explanation: Angle in a semicircle is always a right angle (90°).
12. Angles in the same segment of a circle are:
A. Equal
B. Unequal
C. Supplementary
D. Complementary
Answer: A. Equal
Explanation: Theorem 10.9 states that angles in the same segment of a circle are equal.
13. The sum of either pair of opposite angles of a cyclic quadrilateral is:
A. 90°
B. 180°
C. 270°
D. 360°
Answer: B. 180°
Explanation: Theorem 10.11 states that the opposite angles of a cyclic quadrilateral are supplementary (180°).
14. If a quadrilateral ABCD is cyclic, and ∠A = 70°, find ∠C.
A. 70°
B. 110°
C. 90°
D. 120°
Answer: B. 110°
Explanation: In a cyclic quadrilateral, opposite angles sum to 180°. So ∠C = 180° - 70° = 110°.
15. If the radius of a circle is 5 cm and a chord is at a distance of 3 cm from the center, the length of the chord is:
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Answer: C. 8 cm
Explanation: Half chord = √(5² - 3²) = √(25 - 9) = √16 = 4 cm. Full chord length = 2 × 4 = 8 cm.
16. Chords equidistant from the center of a circle are ________ in length.
A. Unequal
B. Double
C. Equal
D. Half
Answer: C. Equal
Explanation: Theorem 10.6 states that chords equidistant from the center are equal in length.
17. If an arc subtends an angle of 80° at the center of a circle, what angle does it subtend at the circumference?
A. 160°
B. 40°
C. 80°
D. 20°
Answer: B. 40°
Explanation: Angle at circumference = 1/2 × Angle at center = 1/2 × 80° = 40°.
18. A cyclic parallelogram is always a:
A. Rhombus
B. Rectangle
C. Trapezium
D. Kite
Answer: B. Rectangle
Explanation: Opposite angles of a parallelogram are equal. Since it's cyclic, their sum is 180°. So each angle = 90°, making it a rectangle.
19. If the length of a chord of a circle of radius 10 cm is 16 cm, find its distance from the center.
A. 6 cm
B. 8 cm
C. 12 cm
D. 5 cm
Answer: A. 6 cm
Explanation: Half chord = 8 cm. Distance from center = √(10² - 8²) = √(100 - 64) = √36 = 6 cm.
20. Sector of a circle is the region between an arc and ________ radii.
A. One
B. Two
C. Three
D. Four
Answer: B. Two
Explanation: A sector is bounded by two radii joining the center to the endpoints of an arc.
21. In a cyclic quadrilateral ABCD, if ∠A = 2x and ∠C = 3x, find x.
This page contains a chapter-wise objective practice set. Try the questions without checking the answer first, then use the explanation to understand the point you missed. The current page contains 30 questions, so you can practise in smaller sets when you are revising.
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