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Vidaara.orgClass 9 · Mathematics
CodeVID-M9-10-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.
The longest chord of a circle is the:
  • A.radius
  • B.diameter
  • C.arc
  • D.tangent
2.
The perpendicular from the centre to a chord:
  • A.doubles it
  • B.bisects it
  • C.is parallel
  • D.equals it
3.
Opposite angles of a cyclic quadrilateral sum to:
  • A.$90^\circ$
  • B.$180^\circ$
  • C.$270^\circ$
  • D.$360^\circ$
4.
The diameter is ___ the radius.
  • A.half
  • B.twice
  • C.equal to
  • D.four times
5.
Equal chords are equidistant from the:
  • A.circumference
  • B.centre
  • C.diameter
  • D.tangent
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If the radius is $7$, find the diameter.
7.
A chord is $16$ cm; the perpendicular from the centre bisects it into:
8.
One angle of a cyclic quadrilateral is $70^\circ$. Find the opposite angle.
9.
If the diameter is $10$, find the radius.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Define a chord.
11.
A chord of length $24$ cm is $5$ cm from the centre. Find the radius.
12.
In cyclic quadrilateral $ABCD$, $\angle A=85^\circ$, $\angle B=95^\circ$. Find $\angle C$ and $\angle D$.
13.
The radius is $8$ cm; find the diameter.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Define: radius, diameter, chord, arc and sector (one line each).
15.
A chord of a circle of radius $13$ cm is at a distance of $5$ cm from the centre. Find the length of the chord.

Answer Key

Section A — Multiple Choice Questions
  1. (B) diameter
  2. (B) bisects it
  3. (B) $180^\circ$
  4. (B) twice
  5. (B) centre
Section B — Short Answer (2 marks)
  1. $14$.
  2. $8$ cm each.
  3. $110^\circ$.
  4. $5$.
Section C — Short Answer (3 marks)
  1. A segment joining two points on the circle.
  2. $13$ cm.
  3. $\angle C=95^\circ,\ \angle D=85^\circ$.
  4. $16$ cm.
Section D — Long Answer (5 marks)
  1. Radius: centre to circle; diameter: longest chord through the centre ($=2r$); chord: segment joining two points; arc: part of the circumference; sector: region between two radii and an arc.
  2. $24$ cm.
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