CBSE Questions for Class 9 Maths Circles Quiz 2 - MCQExams.com

A square is inscribed in the circle $${ x }^{ 2 }+{ y }^{ 2 }-6x+8y-103=0$$ with its sides parallel to the coordinate axes . Then the distance of the vertex of this square which is nearest to the origin is :
  • 6
  • $$\sqrt { 137 } $$
  • $$\sqrt { 41 } $$
  • 13
In the give figure, ABCD is a cyclic quadrilateral, $$
\angle C B Q=48^{\circ}
 $$ and a=2b. Then, b is equal to

1361006_910b72447c7b47b3888b16134f24c46a.png
  • $$

    48^{\circ}

    $$
  • $$

    38^{\circ}

    $$
  • $$

    28^{\circ}

    $$
  • none of these
The value of x and y in tyhe fighure are measure of angles,then x+y is equal to 
1493360_4fc19407c836410381dcfcfa439d3c76.PNG
  • $$
    90^{\circ}
    $$
  • $$
    85^{\circ}
    $$
  • $$
    75^{\circ}
    $$
  • $$
    65^{\circ}
    $$
Distance between chords of contact of the tangents of the circle $$ x ^ { 2 } + y ^ { 2 } + 2 y x + 27 y + c = 0 $$ from the origin and the point ($$g, f$$) is
  • $$ \sqrt { g ^ { 2 } + f ^ { 2 } } $$
  • $$ \frac { \sqrt { g ^ { 2 } + f ^ { 2 } - c } } { 2 } $$
  • $$ \frac { g ^ { 2 } + f ^ { 2 } - c } { 2 \sqrt { g ^ { 2 } + f ^ { 2 } } } $$
  • $$ \frac { \sqrt { g ^ { 2 } + f ^ { 2 } + c } } { 2 \sqrt { g ^ { 2 } + f ^ { 2 } } } $$
$$ AB C D$$ is cyclic quadrilateral such that $$AB$$ is a diameter of the circle circumscribing it and $$\angle ADC=130^{ { \circ  } },$$ then the value of $$\angle A B C$$ is:
  • $$50 ^ { \circ }$$
  • $$60 ^ { \circ }$$
  • $$120 ^ { \circ }$$
  • $$40 ^ { \circ }$$
What will be the area of the largest square that can be cut out of a circle of radius 10 cm?
  • 100 $${ cm }^{ 2 }$$
  • 200 $${ cm }^{ 2 }$$
  • 300 $${ cm }^{ 2 }$$
  • 400 $${ cm }^{ 2 }$$
$$\Box ABCD$$ is a cyclic quadrilateral, $$\angle BAD={ 75 }^{ \circ  },m\angle ADC={ 85 }^{ \circ  }$$. The bisectors of $$\angle ABC$$ and $$\angle BCD$$ meet in the point O. Find m$$\angle BOC.$$
1488957_a1b468aaf86949419d0e56b1e85ea9bf.PNG
  • $${ 40 }^{ \circ }$$
  • $${ 70 }^{ \circ }$$
  • $${ 80 }^{ \circ }$$
  • $${ 60 }^{ \circ }$$
A,B,C and D be the angles of cyclic quadrilateral taken order , then $$cos({ 180 }^{ \circ  }+A)$$ + $$cos({ 180 }^{ \circ  }+B)$$+$$cos({ 180 }^{ \circ  }+C)$$+$$cos({ 180 }^{ \circ  }+D)$$is equal to 
  • 2 (cosA+cosB )
  • 2 (cosA+cosD)
  • 0
  • 4 cos A
Consider a circle with center O and radius = 20cm. Find the perpendicular distance of a chord of length 32cm from the center of the circle.
  • 20cm
  • 18cm
  • 14cm
  • 12cm
Write True or False and justify your answer in each of the following : 
If $$A , B , C$$ and $$D$$ are four points such that $$ \angle BAC$$  $$ =45^{\circ} $$ and $$ \angle $$ BDC = $$ 45^{\circ} $$ , then $$A , B , C , D $$ are concyclic. 
  • True
  • False
Write True or False and justify your answer in each of the following : 
If $$A , B , C , D$$ are four points such that $$ \angle BAC$$ $$= 30^{\circ} $$ and $$ \angle $$ BDC = $$ 60^{\circ} $$, then $$D$$ is the center of the circle through $$A , B$$ and $$C$$. 
  • True
  • False
Consider a circle with center O and radius = 25cm. Find the perpendicular distance of a chord of length 14cm from the center of the circle.
  • $$20cm$$
  • $$24cm$$
  • $$18cm$$
  • $$14cm$$
Consider a chord $$AB = 10cm$$, of a circle with radius $$r$$. A line segment $$OM = 3cm$$ from the center O of the circle to AB, bisects AB into two equal parts.
Then what is the value of $$r$$?
  • $$\sqrt {40}$$
  • $$\sqrt {35}$$
  • $$\sqrt {34}$$
  • $$\sqrt {50}$$
Consider a chord $$AB = 24cm$$, of a circle with radius $$r$$. A line segment $$OM = 5cm$$ from the center O of the circle to AB, bisects AB into two equal parts.
Then what is the value of $$r$$?
  • $$13 cm$$
  • $$24 \sqrt 2cm$$
  • $$20cm$$
  • $$ 19 cm$$
Consider a circle with center O and radius = 13cm. Find the perpendicular distance of a chord of length 10cm from the center of the circle.
  • 8cm
  • 10cm
  • 12cm
  • 15cm
Consider a chord $$AB = 8cm$$, of a circle with radius $$r$$. A line segment $$OM = 3cm$$ from the center O of the circle to AB, bisects AB into two equal parts.
Then what is the value of $$r$$?
  • $$3 \sqrt 2cm$$
  • $$\sqrt 71cm$$
  • $$5cm$$
  • $$4 \sqrt 2cm$$
To prove "The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord", we prove congruence of which two triangles?
1949200_ba725b726bfa4573b38b223373d4e9a6.png
  • $$\triangle AOM \ and \ \triangle BOM$$
  • $$\triangle AOM \ and \ \triangle BOA$$
  • $$\triangle AOB \ and \ \triangle BOM$$
  • $$\triangle AOM \ and \ \triangle MOB$$
How many circles pass through 3 non-colinear given points?
  • 1
  • 2
  • More than 2
  • Infinitely many
In given figure, is possible to draw another circle using points $$X, Y$$ and $$Z$$ which will be different from given circle?
1949329_f2836460fa454bc8a0aed3a6ac0f580a.png
  • Yes
  • No
  • Can't say anything
  • None of these
How many circles can be drawn using given three collinear points?
  • 0
  • 1
  • 4
  • Infinitely
If three points are collinear, then we can draw a circle using given points.
  • True
  • False
  • May be
  • None of these
In the given image, in which of figure, we can draw another circle using the vertices of triangle different from already existing circle?
1949325_ba7b166cc90b4dd9992faec5f8dd088a.jpg
  • Figure 1
  • Figure 2
  • Figure 3
  • Not possible in any of the figure
Which of the following pair of angles are opposite angles of a cyclic quadrilateral?
  • $$131^{\circ}, 28^{\circ}$$
  • $$95^{\circ}, 55^{\circ}$$
  • $$123^{\circ}, 57^{\circ}$$
  • $$64^{\circ}, 52^{\circ}$$
In Fig 10.9 $$\displaystyle \angle AOB= 90^{\circ}\,and\,\angle ABC=30^{\circ}\,then\,\angle CAO$$ is equal to
426581_aa2123a5c0184e5d9cccccaf7b979e22.png
  • $$\displaystyle 30^{\circ}$$
  • $$\displaystyle 45^{\circ}$$
  • $$\displaystyle 90^{\circ}$$
  • $$\displaystyle 60^{\circ}$$
In the given figure $$O$$ is the centre of the circle and $$\displaystyle \angle AOC=120^{\circ}$$. What is the value of $$\displaystyle \angle APC+\angle ABC$$?
377062_cc70f77620da4e09809a07dae33231b2.png
  • $$\displaystyle 120^{\circ}$$
  • $$\displaystyle 140^{\circ}$$
  • $$\displaystyle 160^{\circ}$$
  • $$\displaystyle 180^{\circ}$$
Fixed point in the circle is called _____ of the circle.
  • radius
  • centre
  • diameter
  • none
In Fig 10.7 if $$\displaystyle \angle DAB=60^{\circ},\angle ABD= 50^{\circ}$$ then $$\displaystyle \angle ACB$$ is equal to
426563_09bcf2c596d1412a94cb41733ec56b50.png
  • $$\displaystyle 60^{\circ}$$
  • $$\displaystyle 50^{\circ}$$
  • $$\displaystyle 70^{\circ}$$
  • $$\displaystyle 80^{\circ}$$
In the given figure, $$\displaystyle \triangle ABC$$ is an equilateral triangle. What is the value of $$\displaystyle \angle BEC$$?
377054_0920df7cca9f4150b22efcbabfdc0133.png
  • $$\displaystyle 80^{\circ}$$
  • $$\displaystyle 100^{\circ}$$
  • $$\displaystyle 120^{\circ}$$
  • $$\displaystyle 130^{\circ}$$
If an equilateral triangle inscribed in a circle with center $$O$$, then the measure of $$\angle AOB $$ is
  • $$60$$
  • $$90$$
  • $$120$$
  • $$180$$
In Fig 10.4 if $$\displaystyle \angle ABC = 20^{\circ}$$ then $$\displaystyle \angle AOC $$ is equal to
426545_933df1c79a414e3d8092159c0ec56a47.png
  • $$\displaystyle 20^{\circ}$$
  • $$\displaystyle 40^{\circ}$$
  • $$\displaystyle 60^{\circ}$$
  • $$\displaystyle 10^{\circ}$$
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