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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-08-INT-01
Introduction to Circles & Tangents — Assignment
Chapter: Circles
Topic: Introduction to Circles & Tangents
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
A tangent touches a circle at:
  • A.one point
  • B.two points
  • C.no point
  • D.three points
2.
A line meets a circle in at most:
  • A.$1$
  • B.$2$
  • C.$3$
  • D.$0$ points
3.
The number of tangents from an external point is:
  • A.$0$
  • B.$1$
  • C.$2$
  • D.infinite
4.
The number of tangents at a point on the circle is:
  • A.$0$
  • B.$1$
  • C.$2$
  • D.infinite
5.
A secant meets a circle in:
  • A.$1$ point
  • B.$2$ points
  • C.$0$ points
  • D.$3$ points
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
How many tangents can be drawn from an external point?
7.
How many tangents can be drawn at a point on the circle?
8.
What is a line that touches a circle at exactly one point called?
9.
How many common tangents do two externally touching circles have?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
State the relationship between a tangent and the radius at the point of contact.
11.
From a point $10$ cm from the centre of a circle of radius $6$ cm, find the length of the tangent.
12.
How many tangents to a circle are parallel to a given line?
13.
Two concentric circles have radii $5$ and $3$; a chord of the larger touches the smaller. Find its length.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The length of a tangent from a point $13$ cm from the centre is $12$ cm. Find the radius.
15.
Two concentric circles have radii $13$ cm and $5$ cm. Find the length of the chord of the larger circle that touches the smaller circle.

Answer Key

Section A — Multiple Choice Questions
  1. (A) one point
  2. (B) $2$
  3. (C) $2$
  4. (B) $1$
  5. (B) $2$ points
Section B — Short Answer (2 marks)
  1. $2$.
  2. $1$.
  3. A tangent.
  4. $3$.
Section C — Short Answer (3 marks)
  1. They are perpendicular.
  2. $8$ cm.
  3. $2$.
  4. $8$.
Section D — Long Answer (5 marks)
  1. $5$ cm.
  2. $24$ cm.
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