Circles Practice Questions
Class 9 · Mathematics · 2312 free MCQs with instant results and detailed explanations.
2312
Total
682
Easy
1118
Medium
512
Hard
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Topics in Circles
Angle Subtended by Chord
650
Perpendicular from Centre
959
Cyclic Quadrilateral
703
Sample Questions from Circles
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
What is the relationship between the radius of a circle and any perpendicular drawn from the center to the circumference?
A.
The radius is equal to the length of the perpendicular.
B.
The radius is greater than the length of the perpendicular.
C.
The perpendicular bisects the radius.
D.
The length of the perpendicular is always zero.
Show Answer & Explanation
Correct Answer: A
A perpendicular drawn from the center of a circle to a chord is equal to the length of the radius.
Q2
Easy
If a circle has a radius of 5 cm, what is the length of a perpendicular from the center to a point on the circumference?
A.
0 cm
B.
5 cm
C.
10 cm
D.
2.5 cm
Show Answer & Explanation
Correct Answer: B
The perpendicular from the center to the circumference is equal to the radius, which is 5 cm.
Q3
Easy
In a circle, if a radius is drawn to a point where a perpendicular meets the circumference, what can we say about the angles formed?
A.
They are all 90 degrees.
B.
The radius and the perpendicular do not form any angles.
C.
The angle between the radius and the perpendicular is 90 degrees.
D.
The angles are acute.
Show Answer & Explanation
Correct Answer: C
The radius drawn to the point of tangency with the perpendicular forms a right angle (90 degrees).
Q4
Medium
A chord AB of a circle subtends an angle of 120° at the center. What is the angle subtended by the chord at a point C on the circle not on the same side as the center?
A.
60°
B.
30°
C.
120°
D.
90°
Show Answer & Explanation
Correct Answer: B
The angle subtended opposite the chord is equal to the angle subtended at the center. Hence, angle = 180° - (120° / 2) = 30°.
Q5
Medium
In a circle, a chord AB subtends an angle of 60° at the center. What is the angle subtended by chord AB at a point on the circumference that is not on the same side as the center?
A.
60°
B.
120°
C.
30°
D.
90°
Show Answer & Explanation
Correct Answer: C
The angle subtended at the opposite side is equal to the angle subtended at the center subtracted from 180°, so angle = 180° - (60° / 2) = 30°.
Q6
Medium
A chord PQ subtends an angle of 160° at the center. What is the angle subtended at point R on the circumference not on the same side as the center?
A.
80°
B.
20°
C.
90°
D.
40°
Show Answer & Explanation
Correct Answer: B
The angle subtended at the opposite side is 180° - (angle at center / 2). Thus, angle = 180° - (160° / 2) = 20°.
Q7
Medium
In a circle, two chords AB and CD intersect at point P. If angle APB measures 40 degrees and angle CPD measures 60 degrees, what is the measure of angle APD?
A.
20 degrees
B.
30 degrees
C.
50 degrees
D.
70 degrees
Show Answer & Explanation
Correct Answer: C
Angle APD is equal to half the difference of the angles subtended by the chords at the circumference, which is (60 - 40)/2 = 10 degrees. Thus, APD = APB + 10 = 50 degrees.
Q8
Hard
In a circle, if the angle subtended by a chord at the center is 60°, what is the angle subtended by the same chord at any point on the remaining part of the circle?
A.
30°
B.
60°
C.
90°
D.
120°
Show Answer & Explanation
Correct Answer: A
The angle subtended by the chord at any point on the circle is half of the angle subtended at the center. Thus, it is 60°/2 = 30°.
Q9
Hard
A chord AB of a circle subtends an angle of 50° at a point C on the circle. What is the angle subtended by chord AB at the center of the circle?
A.
100°
B.
50°
C.
25°
D.
75°
Show Answer & Explanation
Correct Answer: A
The angle at the center is twice the angle at the circumference. Therefore, 50° * 2 = 100°.
Q10
Hard
If the angle subtended by a chord at a point on the circumference is 70°, what is the relationship between this angle and the angle subtended at the center?
A.
It is equal
B.
It is half
C.
It is double
D.
It is three times
Show Answer & Explanation
Correct Answer: C
The angle subtended at the center is always double the angle subtended at the circumference by the same chord.
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Circles — Class 9 Mathematics Practice Questions Online
This page contains 2312 practice MCQs for the chapter Circles in Class 9 Mathematics. The questions are organized by difficulty — 682 easy, 1118 medium, 512 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.