Welcome to the Class 9 Chapter 10 (Circles) Revision & PYQ Chapter Quiz!
Boost your preparation for Class 9 exams and competitive tests like RRB NTPC, SSC CGL, and SSC GD. Answer the high-yield questions below to test your understanding of chord properties, angle subtensions, and cyclic quadrilaterals.
Q1. A chord of length 10 cm is at a distance of 12 cm from the center of a circle. What is the radius of the circle?
A) 10 cm
B) 13 cm
C) 15 cm
D) 17 cm
Show Solution
Correct Answer: B) 13 cm
Step-by-step Solution:
1. The perpendicular drawn from the center of a circle to a chord bisects the chord.
2. Half chord length = 10 / 2 = 5 cm.
3. Perpendicular distance = 12 cm.
4. Using Pythagoras theorem: Radius² = (5)² + (12)² = 25 + 144 = 169.
5. Radius = √169 = 13 cm.
Q2. If a chord AB of length 8 cm subtends an angle of 60° at the center O of a circle, what is the radius of the circle?
A) 4 cm
B) 8 cm
C) 8√3 cm
D) 16 cm
Show Solution
Correct Answer: B) 8 cm
Step-by-step Solution:
1. In △OAB, OA = OB = radius (r).
2. Angles opposite to equal sides are equal, so ∠OAB = ∠OBA.
3. Since ∠AOB = 60°, ∠OAB + ∠OBA = 180° - 60° = 120°, making each angle 60°.
4. Thus, △OAB is an equilateral triangle with AB = OA = OB = 8 cm.
5. Radius = 8 cm.
Q3. ABCD is a cyclic quadrilateral where ∠ABC = 75°. What is the measure of the opposite angle ∠ADC?
A) 75°
B) 90°
C) 105°
D) 115°
Show Solution
Correct Answer: C) 105°
Step-by-step Solution:
1. The sum of opposite angles in a cyclic quadrilateral is always 180°.
2. ∠ABC + ∠ADC = 180°.
3. ∠ADC = 180° - 75° = 105°.
Q4. What is the angle subtended by a diameter at any point on the circle (angle in a semicircle)?
A) 45°
B) 60°
C) 90°
D) 180°
Show Solution
Correct Answer: C) 90°
Step-by-step Solution:
1. The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
2. A diameter subtends a straight angle (180°) at the center.
3. Therefore, angle at any point on the semicircle = 180° / 2 = 90°.
Q5. Two equal circles of radius 5 cm intersect each other, and the length of their common chord is 6 cm. What is the distance between their centers?
A) 6 cm
B) 8 cm
C) 10 cm
D) 12 cm
Show Solution
Correct Answer: B) 8 cm
Step-by-step Solution:
1. The line joining the centers is the perpendicular bisector of the common chord.
2. Half length of common chord = 6 / 2 = 3 cm.
3. Distance from one center to chord line = √(5² - 3²) = √(25 - 9) = √16 = 4 cm.
4. Since both circles are equal, total distance between centers = 4 cm + 4 cm = 8 cm.
Great job completing the Class 9 Chapter 10 Circles quiz! Revising these core concepts and PYQs regularly ensures top scores in both school exams and competitive tests like RRB, SSC, and GD.
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