Circles CBSE Questions & Answers

Circles

This is Mathematics Class 09 Circles CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. If \(\angle BEF = {80^o}\), then \(\angle ABC\) is equal to
Question 1 figure 1
  • A
    \({120^o}\)
  • B
    \({75^o}\)
  • C
    \({80^o}\)
    Correct
  • D
    \({100^o}\)
2
If a chord of a circle is equal to its radius, then the angle subtended by this chord in major segment is
  • A
    \({45^o}\)
  • B
    \({90^o}\)
  • C
    \({60^o}\)
  • D
    \({30^o}\)
    Correct
3
In the given figure PQ and RS are two equal chords of a circle with centre O. OA and OB are perpendiculars on chords PQ and RS, respectively. If \(\angle AOB = {140^o},\) then \(\angle PAB\) is equal to
Question 3 figure 1
  • A
    \({60^o}\)
  • B
    \({40^o}\)
  • C
    \({70^o}\)
    Correct
  • D
    \({50^o}\)
4
In the given figure PQ = QR = RS and \(\angle PTS = {75^o}\) then the measure of \(\angle QOR\) is
Question 4 figure 1
  • A
    \({20^o}\)
  • B
    \({75^o}\)
  • C
    \({25^o}\)
  • D
    \({50^o}\)
    Correct
5
In the given figure, if \(\angle ABC = {50^o}\) and \(\angle BDC = {40^o}\), then \(\angle BCA\) is equal to
Question 5 figure 1
  • A
    \({50^o}\)
  • B
    \({90^o}\)
    Correct
  • C
    \({40^o}\)
  • D
    \({100^o}\)
6
In the given figure, AC is a diameter of the given circle and \(\angle BCD = {75^o}\) . Then, \(\angle EAF - \angle ABC\) is equal to
Question 6 figure 1
  • A
    \({10^o}\)
  • B
    \({20^o}\)
  • C
    \({15^o}\)
    Correct
  • D
    \({25^o}\)
7
In the given figure, O is the centre of the circle. \(\angle OAB\) and \(\angle OCB\) are \({40^o}\) and \({30^o}\) respectively. Then, the measure of \(\angle AOC\) is
Question 7 figure 1
  • A
    \({140^o}\)
    Correct
  • B
    \({120^o}\)
  • C
    \({170^o}\)
  • D
    \({110^o}\)
8
If \(\angle OAB = {40^o},\) then the measure of \(\angle ACB\) is
Question 8 figure 1
  • A
    \({20^o}\)
  • B
    \({50^o}\)
    Correct
  • C
    \({80^o}\)
  • D
    \({40^o}\)
9
BC is a diameter of the circle and \(\angle BAO = {60^o}\) . Then \(\angle ADC\) is equal to
Question 9 figure 1
  • A
    \({45^o}\)
  • B
    \({90^o}\)
  • C
    \({30^o}\)
  • D
    \({60^o}\)
    Correct
10
In the given figure, O is the centre of the circle and \(\angle AOC = {130^o}\) . Then \(\angle ABC\) is equal to
Question 10 figure 1
  • A
    \({65^o}\)
  • B
    \({165^o}\)
  • C
    \({130^o}\)
  • D
    \({115^o}\)
    Correct
11
In the given figure , if \(\angle CAB = {50^o}\) and \(\angle CAB = {70^o},\) then \(\angle ADB\) is equal to
Question 11 figure 1
  • A
    \({80^ \circ }\)
  • B
    \({70^ \circ }\)
  • C
    \({60^ \circ }\)
    Correct
  • D
    \({50^ \circ }\)
12
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and \(\angle ADC = {140^o},\) then \(\angle BAC\) is equal to
  • A
    \({75^o}\)
  • B
    \({40^o}\)
  • C
    \({30^o}\)
  • D
    \({50^o}\)
    Correct
13
In the given figure \(\angle ABC = {45^o}\), then the measure of \(\angle AOC\) is
Question 13 figure 1
  • A
    \({75^o}\)
  • B
    \({60^o}\)
  • C
    \({90^o}\)
    Correct
  • D
    \({45^o}\)
14
O is the centre of the given circle. If \(\angle APB = {120^o}\) and \(\angle DBC = {25^o}\), then the measure of \(\angle ADB\) is equal to
Question 14 figure 1
  • A
    \({95^o}\)
    Correct
  • B
    \({120^o}\)
  • C
    \({60^o}\)
  • D
    \({100^o}\)
15
In the given figure, O is the centre of the circle. If \(\angle DBA = {35^o}\) , then the measure of \(\angle ACB\) is equal to
Question 15 figure 1
  • A
    \({55^o}\)
    Correct
  • B
    \({45^o}\)
  • C
    \({55^o}\)
  • D
    \({65^o}\)