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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-10-CHD-01
Chords & Angles Subtended - Assignment
Chapter: Circles
Topic: Chords, Perpendiculars and Angles Subtended
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.
The perpendicular from the centre to a chord:
  • A.doubles it
  • B.bisects it
  • C.is parallel
  • D.equals it
2.
Equal chords are equidistant from the:
  • A.circumference
  • B.centre
  • C.diameter
  • D.tangent
3.
The central angle is ___ the inscribed angle on the same arc.
  • A.equal
  • B.twice
  • C.half
  • D.thrice
4.
Angles in the same segment are:
  • A.supplementary
  • B.equal
  • C.complementary
  • D.right
5.
The angle in a semicircle is:
  • A.$45^\circ$
  • B.$60^\circ$
  • C.$90^\circ$
  • D.$180^\circ$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
A chord is $16$ cm; the perpendicular from the centre bisects it into:
7.
If the inscribed angle is $40^\circ$, find the central angle on the same arc.
8.
What is the angle in a semicircle?
9.
Equal chords are equidistant from which point?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
A chord of length $24$ cm is $5$ cm from the centre. Find the radius.
11.
An arc subtends $100^\circ$ at the centre. Find the inscribed angle on the same arc.
12.
Two equal chords subtend equal angles at which point?
13.
The inscribed angle in the major segment is $50^\circ$. Find the central angle.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
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.
15.
An arc subtends $130^\circ$ at the centre. Find the angle it subtends at a point on the major arc.

Answer Key

Section A — Multiple Choice Questions
  1. (B) bisects it
  2. (B) centre
  3. (B) twice
  4. (B) equal
  5. (C) $90^\circ$
Section B — Short Answer (2 marks)
  1. $8$ cm each.
  2. $80^\circ$.
  3. $90^\circ$.
  4. The centre.
Section C — Short Answer (3 marks)
  1. $13$ cm.
  2. $50^\circ$.
  3. The centre.
  4. $100^\circ$.
Section D — Long Answer (5 marks)
  1. $24$ cm.
  2. $65^\circ$.
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