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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-08-CT
Circles — Full Chapter Test
Chapter: Circles
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
The tangent is ___ to the radius at the point of contact.
  • A.parallel
  • B.perpendicular
  • C.equal
  • D.oblique
3.
Tangents from an external point are:
  • A.equal
  • B.unequal
  • C.perpendicular
  • D.parallel
4.
A line meets a circle in at most:
  • A.$1$
  • B.$2$
  • C.$3$
  • D.$0$ points
5.
The tangent length (distance $d$, radius $r$) is:
  • A.$\sqrt{d^2-r^2}$
  • B.$\sqrt{d^2+r^2}$
  • C.$d-r$
  • D.$dr$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
How many tangents can be drawn from an external point?
7.
State the tangent–radius theorem.
8.
Find the tangent length from a point $17$ cm from the centre, radius $8$ cm.
9.
How many tangents can be drawn at a point on the circle?
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.
$PA$ and $PB$ are tangents from $P$ to a circle with centre $O$. If $\angle APB=60^\circ$, find $\angle AOB$.
12.
An incircle touches $BC,CA,AB$ at $D,E,F$ with $BD=4,\ CE=5,\ AF=3$. Find the sides $AB,BC,CA$.
13.
From a point $10$ cm from the centre of a circle of radius $6$ cm, find the length of the tangent.
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 tangents $TP$ and $TQ$ are drawn from an external point $T$ to a circle with centre $O$. Prove that $\angle PTQ=2\angle OPQ$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) one point
  2. (B) perpendicular
  3. (A) equal
  4. (B) $2$
  5. (A) $\sqrt{d^2-r^2}$
Section B — Short Answer (2 marks)
  1. $2$.
  2. The tangent is perpendicular to the radius at the point of contact.
  3. $15$ cm.
  4. $1$.
Section C — Short Answer (3 marks)
  1. They are perpendicular.
  2. $120^\circ$.
  3. $AB=7,\ BC=9,\ CA=8$.
  4. $8$ cm.
Section D — Long Answer (5 marks)
  1. $5$ cm.
  2. $\angle PTQ=2\angle OPQ$.
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