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
In the given figure, ABCD is a quadrilateral inscribed in circle with centre O. CD is produced to E. If \(\angle ADE = {95^o}\) and \(\angle OBA = {30^o},\) then \(\angle OAC\) is equal to
Question 1 figure 1
  • A
    \({20^o}\)
  • B
    \({15^o}\)
  • C
    \({5^o}\)
    Correct
  • D
    \({10^o}\)
2
In the given figure, ABCD is a cyclic quadrilateral in which \(\angle BAD = {75^o},\) \(\angle ABD = {58^o}\) and \(\angle ADC = {77^o}\) , AC and BD intersect at P. the measure of \(\angle DPC\) is
Question 2 figure 1
  • A
    \({90^o}\)
  • B
    \({92^o}\)
    Correct
  • C
    \({94^o}\)
  • D
    \({105^o}\)
3
AD is diameter of a circle and AB is a chord. If AD = 50 cm, AB = 48 cm, then the distance of AB from the centre of the circle is
  • A
    6 cm
  • B
    7 cm
    Correct
  • C
    5 cm
  • D
    8 cm
4
The given figure shows two congruent circles with centre O and O’ intersecting at A and B. If \(\angle AO'B = {50^o},\) then the measure of \(\angle APB\) is
Question 4 figure 1
  • A
    \({45^o}\)
  • B
    \({50^o}\)
  • C
    \({25^o}\)
    Correct
  • D
    \({40^o}\)
5
In the given figure if \(\angle CAB = {49^o}\)\(\angle CAB = {49^o}\) and \(\angle ADC = {43^o},\) then the measure of \(\angle ACB\) is
Question 5 figure 1
  • A
    \({96^o}\)
  • B
    \({74^o}\)
  • C
    \({92^o}\)
  • D
    \({88^o}\)
    Correct
6
P is a point on the diameter AB of a circle and CD is a chord perpendicular to AB. If AP = 4 cm and PB = 16 cm, the length of chord CD is
Question 6 figure 1
  • A
    16 cm
    Correct
  • B
    8 cm
  • C
    10 cm
  • D
    20 cm
7
In the given figure, if \(\angle AOB = {80^o}\) and \(\angle ABC = {30^o}\) , then \(\angle CAO\) is equal to
Question 7 figure 1
  • A
    \({40^o}\)
  • B
    \({30^o}\)
  • C
    \({60^o}\)
    Correct
  • D
    \({80^o}\)
8
In the given figure, AB is a diameter of the circle APBR. APQ and RBQ are straight lines. If \(\angle A = {35^o}\) and , then the measure of \(\angle PBR\) is
Question 8 figure 1
  • A
    \({115^o}\)
    Correct
  • B
    \({155^o}\)
  • C
    \({165^o}\)
  • D
    \({135^o}\)
9
In the given figure, AD is the diameter of the circle and AE=DE. If \(\angle ABC = {115^o},\) then the measure of \(\angle CAE\) is
Question 9 figure 1
  • A
    \({80^o}\)
  • B
    \({90^o}\)
  • C
    \({70^o}\)
    Correct
  • D
    \({60^o}\)
10
AOB is the diameter of the circle. If \(\angle AOE = {150^o},\) then the measure of \(\angle CBE\) is
Question 10 figure 1
  • A
    \({125^o}\)
  • B
    \({115^o}\)
  • C
    \({105^o}\)
    Correct
  • D
    \({120^o}\)
11
In the given figure, P and Q are centers of two circles intersecting at B and C. ACD is a straight line. Then, the measure of \(\angle BQD\) is
Question 11 figure 1
  • A
    \({115^o}\)
  • B
    \({105^o}\)
  • C
    \({150^o}\)
    Correct
  • D
    \({130^o}\)
12
The figure shows two circles which intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle. If \(\angle APB = {70^o},\) then the measure of \(\angle ACB\) is
Question 12 figure 1
  • A
    \({50^o}\)
  • B
    \({50^o}\)
  • C
    \({70^o}\)
  • D
    \({40^o}\)
    Correct
13
AOB is a diameter of the circle and C, D, E are any three points on the semicircle. Then \(\angle AED + \angle BCD\) is equal to
Question 13 figure 1
  • A
    \({250^o}\)
  • B
    \({260^o}\)
  • C
    \({270^o}\)
    Correct
  • D
    \({280^o}\)
14
AOB is the diameter of the circle. ABCD is a cyclic trapezium in which AB \(\parallel \) DC. If \(\angle BED = {65^o}\) , then \(\angle BDC\) is equal to
Question 14 figure 1
  • A
    \({40^o}\)
  • B
    \({75^o}\)
  • C
    \({25^o}\)
    Correct
  • D
    \({65^o}\)
15
In the given figure, AD is a diameter of the circle with centre O. Chords AB, BC and CD are equal. If \(\angle DEF = {110^o},\) then \(\angle FAB\) is equal to
Question 15 figure 1
  • A
    \({120^o}\)
  • B
    \({140^o}\)
  • C
    \({110^o}\)
  • D
    \({130^o}\)
    Correct