Circles Practice Questions
Class 10 · Mathematics · 1385 free MCQs with instant results and detailed explanations.
1385
Total
546
Easy
652
Medium
187
Hard
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Topics in Circles
Tangent to a Circle
450
Properties of Tangents
471
Number of Tangents from a Point
464
Sample Questions from Circles
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
A line touches a circle at exactly one point. What is this line called?
A.
Tangent
B.
Chord
C.
Secant
D.
Diameter
Show Answer & Explanation
Correct Answer: A
A tangent touches a circle at one point only, while a chord and secant intersect the circle at two points.
Q2
Easy
Which of the following statements is true regarding a tangent to a circle?
A.
It can intersect the circle at two points.
B.
It can never touch the circle.
C.
It touches the circle at exactly one point.
D.
It is always longer than the radius.
Show Answer & Explanation
Correct Answer: C
A tangent by definition touches a circle at only one point, distinguishing it from secants or chords that intersect at multiple points.
Q3
Easy
If two tangents are drawn to a circle from a point outside the circle, what can be said about their lengths?
A.
They are always equal.
B.
They vary in length.
C.
One is longer than the other.
D.
Their lengths are not related.
Show Answer & Explanation
Correct Answer: A
The lengths of tangents drawn from an external point to a circle are always equal.
Q4
Medium
If two tangents are drawn from an external point to a circle and the length of each tangent is 10 cm, what is the distance from the external point to the center of the circle?
A.
10√2 cm
B.
10 cm
C.
5√2 cm
D.
20 cm
Show Answer & Explanation
Correct Answer: A
Using the tangent segment theorem, the distance from the external point to the center can be computed using d = √(l² + r²). Here, d = √(10² + 10²) = 10√2.
Q5
Medium
In a circle, a tangent meets a radius at point A. If the radius OA measures 5 cm, what is the measure of angle OAP formed by the radius and the tangent?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show Answer & Explanation
Correct Answer: A
The tangent to a circle is perpendicular to the radius at the point of tangency, forming a right angle (90 degrees).
Q6
Medium
A tangent to a circle is drawn at point P. If the radius at point P is 5 cm, what is the distance from the center of the circle to the tangent line?
A.
5 cm
B.
10 cm
C.
0 cm
D.
Cannot be determined
Show Answer & Explanation
Correct Answer: A
The distance from the center to the tangent line is equal to the radius at the point of tangency.
Q7
Medium
If a line segment AB is a tangent to a circle at point A and the distance from the center O of the circle to point A is 8 cm, what is the length of OA?
A.
8 cm
B.
16 cm
C.
4 cm
D.
10 cm
Show Answer & Explanation
Correct Answer: A
The length OA is equal to the radius of the circle at point A, which is given as 8 cm.
Q8
Hard
If a line segment touches a circle at a point and the radius at that point is perpendicular to the line segment, what is the relationship between the line segment and the radius?
A.
They are equal in length.
B.
They are parallel.
C.
They are perpendicular.
D.
They intersect at two points.
Show Answer & Explanation
Correct Answer: C
A tangent to a circle is always perpendicular to the radius drawn to the point of tangency.
Q9
Hard
In a circle, if two tangents from a point outside the circle are equal, what can be inferred about the position of the point?
A.
It lies on the circle.
B.
It is the center of the circle.
C.
It is outside the circle.
D.
It lies on the diameter.
Show Answer & Explanation
Correct Answer: C
If two tangents are drawn from a point outside the circle, they will always be equal in length, confirming that the point lies outside the circle.
Q10
Hard
A circle is inscribed in a triangle. If one of the tangents drawn from a vertex of the triangle to the circle is 7 cm long, what is the length of the other tangent from the same vertex to the circle?
A.
7 cm
B.
14 cm
C.
10 cm
D.
3 cm
Show Answer & Explanation
Correct Answer: A
From a single external point, the lengths of tangents drawn to a circle are equal. Thus, both tangents from the vertex to the circle are 7 cm.
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Circles — Class 10 Mathematics Practice Questions Online
This page contains 1385 practice MCQs for the chapter Circles in Class 10 Mathematics. The questions are organized by difficulty — 546 easy, 652 medium, 187 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.