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Number of Tangents PYQs

Class 10 Previous Year Questions (2014 – 2026)

Topic Overview

Understand the geometry of tangent existence: 0 from an internal point, 1 from a point on the circle, and exactly 2 from an external point. These are high-scoring VSA and MCQ patterns in board exams.

Q1 2024
00:00
How many tangents can a circle have?
A circle has infinitely many points on its circumference.
Since a tangent can be drawn at every point, a circle has infinitely many tangents.
Ans: Infinite
Q2 2023
00:00
The number of tangents that can be drawn from a point inside a circle is:
(a)(A) 0
(b)(B) 1
(c)(C) 2
(d)(D) infinite
Any line through a point inside a circle will intersect it at two points (secant).
No tangent can exist.
Ans: (A) 0
Q3 2022
00:00
The number of tangents that can be drawn from a point on the circumference of a circle is:
(a)(A) 0
(b)(B) 1
(c)(C) 2
(d)(D) infinite
At any point on the circle, exactly one tangent can be drawn.
Ans: (B) 1
Q4 2022
00:00
The number of tangents drawn from an external point to a circle is:
(a)(A) 1
(b)(B) 2
(c)(C) 3
(d)(D) 4
From an external point, exactly two tangents can be drawn to a circle.
Ans: (B) 2
Q5 2021
00:00
Assertion (A): Two tangents can be drawn to a circle from an external point.
Reason (R): A line meeting a circle at only one point is called a tangent.
Both A and R are true statements, but R is the definition and not the reason why exactly TWO tangents can be drawn (which is due to the geometry of the external point and circle).
However, in standard board marking, they are often marked as related.
Ans: (B) Both A and R are true but R is not the correct explanation
Q6 2020
00:00
The maximum number of parallel tangents a circle can have is:
Parallel tangents must be at the ends of a diameter.
There are only 2 such tangents for any given diameter direction.
Ans: 2
Q7 2024
00:00
Two circles touch each other externally. The number of common tangents to these circles is:
(a)(A) 1
(b)(B) 2
(c)(C) 3
(d)(D) 4
Two direct common tangents and one transverse common tangent at the point of contact.
Total $= 3$.
Ans: (C) 3
Q8 2023
00:00
Two circles touch each other internally. The number of common tangents to these circles is:
(a)(A) 1
(b)(B) 2
(c)(C) 3
(d)(D) 4
Only one common tangent can be drawn at the point of contact.
Ans: (A) 1
00:00
How many tangents can a circle have?
A circle has infinitely many points on its circumference.
Since a tangent can be drawn at every point, a circle has infinitely many tangents.
Ans: Infinite
Q2 2023
00:00
The number of tangents that can be drawn from a point inside a circle is:
(a)(A) 0
(b)(B) 1
(c)(C) 2
(d)(D) infinite
Any line through a point inside a circle will intersect it at two points (secant).
No tangent can exist.
Ans: (A) 0
Q3 2022
00:00
The number of tangents that can be drawn from a point on the circumference of a circle is:
(a)(A) 0
(b)(B) 1
(c)(C) 2
(d)(D) infinite
At any point on the circle, exactly one tangent can be drawn.
Ans: (B) 1
Q4 2022
00:00
The number of tangents drawn from an external point to a circle is:
(a)(A) 1
(b)(B) 2
(c)(C) 3
(d)(D) 4
From an external point, exactly two tangents can be drawn to a circle.
Ans: (B) 2
Q5 2021
00:00
Assertion (A): Two tangents can be drawn to a circle from an external point.
Reason (R): A line meeting a circle at only one point is called a tangent.
Both A and R are true statements, but R is the definition and not the reason why exactly TWO tangents can be drawn (which is due to the geometry of the external point and circle).
However, in standard board marking, they are often marked as related.
Ans: (B) Both A and R are true but R is not the correct explanation
Q6 2020
00:00
The maximum number of parallel tangents a circle can have is:
Parallel tangents must be at the ends of a diameter.
There are only 2 such tangents for any given diameter direction.
Ans: 2
Q7 2024
00:00
Two circles touch each other externally. The number of common tangents to these circles is:
(a)(A) 1
(b)(B) 2
(c)(C) 3
(d)(D) 4
Two direct common tangents and one transverse common tangent at the point of contact.
Total $= 3$.
Ans: (C) 3
Q8 2023
00:00
Two circles touch each other internally. The number of common tangents to these circles is:
(a)(A) 1
(b)(B) 2
(c)(C) 3
(d)(D) 4
Only one common tangent can be drawn at the point of contact.
Ans: (A) 1