MCQ Questions for Class 9 Maths Circles Quiz 8

The shaded portion of the circle represents

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Semicircle
0%
Diameter
0%
A sector of the circle
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Segment

In the given figure, $$ABCD$$ is a cyclic quadrilateral whose side $$AB$$ is a diameter of the circle passing through $$A, B, C$$ and $$D$$. If $$\angle$$ADC$$=130^o$$, find $$\angle$$BAC.

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$$45^o$$
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$$58^o$$
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$$60^o$$
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$$40^o$$

Two chords $$AB$$ and $$CD$$ of lengths $$5\ cm$$ and $$11\ cm$$ respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between $$AB$$ and $$CD$$ is $$6\ cm$$, find the radius of the circle.

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$$\dfrac{5\sqrt{5}}{2}$$
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$$\dfrac{11\sqrt{5}}{2}$$
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$$\dfrac{5\sqrt{5}}{3}$$
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$$\dfrac{5\sqrt{3}}{2}$$

A circle (with centre at O) is touching two intersecting lines AX and BY. The two points of contact A and B subtend an angle of $$65^{\circ}$$ at any point C on the circumference of the circle. If P is the point of intersection of the two lines, then the measure of $$\angle $$ APB is

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$$50^{\circ}$$
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$$65^{\circ}$$
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$$90^{\circ}$$
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$$40^{\circ}$$

In the figure given below, if $$\angle AOP \, = \, 75^\circ$$ and $$\angle AOB \, = \, 120^\circ$$, then what is $$\angle AQP$$ ?

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$$45^{\circ}$$
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$$37.5^{\circ}$$
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$$30^{\circ}$$
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$$22.5^{\circ}$$

$$BD$$ is a chord parallel to the diameter $$AC$$ of a circle. A point $$B$$ is on the perimeter of the circle such that angle $$CBE={ 63 }^{ o }$$. The angle $$DCE$$ is equal to:

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$${ 63 }^{ o }$$
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$${ 36 }^{ o }$$
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$${ 31.5 }^{ o }$$
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$${ 27 }^{ o }$$

In a cyclic quadrilateral $$ ABCD$$, twice the measure of $$\angle A $$ is thrice the measure of $$\angle C$$, find the measure of $$\angle C$$.

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$$36^{o}$$
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$$72^{o}$$
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$$90^{o}$$
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$$108^{o}$$

Quadilateral ABCD is cyclic. If $$ \angle B = 60^o$$, then $$\angle D = $$____.

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$$30^o$$
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$$100^o$$
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$$120^o$$
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$$90^o$$

In the given figure, AD=BC, $$\angle BAC={ 30 }^{ o }$$ and $$\angle CBD={ 70 }^{ o }$$. Find $$\angle BCD$$.

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$$80^0$$
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$$30^0$$
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$$70^0$$
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None of these

A chord divides a circle into two

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Diameter
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Semicircle
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Sectors
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Segments

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

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True
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False

Explanation

$${\textbf{Step-1: Drawing the diagram as per given question and proving the required statement}}$$

$${\text{Here, ABCD is a cyclic quadrilateral}}$$

$${\text{AH, BF, CF and DH are the angle bisectors of}}$$ $$\angle $$ $${\text{A,}}$$ $$\angle $$ $${\text{B,}}$$ $$\angle $$ $${\text{C,}}$$ $$\angle $$ $${\text{D.}}$$

$$\angle $$ $${\text{FEH =}}$$ $$\angle $$ $${\text{AEB ……. (1) [Vertically opposite angles]}}$$

$$\angle $$ $${\text{FGH =}}$$ $$\angle $$ $${\text{DGC.…… (2) [Vertically opposite angles]}}$$

$${\text{Adding (1) and (2),}}$$

$$\angle $$ $${\text{FEH +}}$$ $$\angle $$ $${\text{FGH =}}$$ $$\angle $$ $${\text{AEB + DGC …..(3)}}$$

$${\text{Now, by angle sum property of a triangle,}}$$

$$\angle $$ $${\text{AEB =}}$$ $${\text{18}}{{\text{0}}^{\text{0}}}{\text{ - }}\left( {\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{A + }}\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{B}}} \right)$$ $${\text{…….(4)}}$$

$$\angle {\text{DGC = 18}}{{\text{0}}^{\text{0}}}{\text{ - }}\left( {\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{C + }}\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{D}}} \right)$$ $${\text{………..(5)}}$$

$${\text{Substituting (4) and (5) in equation (3)}}$$

$$\angle {\text{FEH + }}\angle {\text{FGH = 18}}{{\text{0}}^{\text{0}}}{\text{ - }}\left( {\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{A + }}\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{B}}} \right){\text{ + 18}}{{\text{0}}^{\text{0}}}{\text{ - }}\left( {\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{C + }}\dfrac{{\text{1}}}{{\text{2}}}\angle {\text{D}}} \right)$$

$$\angle {\text{FEH + }}\angle {\text{FGH = 36}}{{\text{0}}^{\text{0}}}{\text{ - }}\dfrac{1}{2}\left( {\angle {\text{A + }}\angle {\text{B + }}\angle {\text{C + }}\angle {\text{D}}} \right)$$

$$\angle {\text{FEH + }}\angle {\text{FGH = 36}}{{\text{0}}^{\text{0}}}{\text{ - }}\dfrac{1}{2} \times {360^0}$$

$$\angle {\text{FEH + }}\angle {\text{FGH = 18}}{{\text{0}}^0}$$

$${\text{Now, the sum of opposite angles of quadrilateral EFGH is}}$$ $${\text{18}}{{\text{0}}^0}$$

$${\text{EFGH is a cyclic quadrilateral}}$$

$${\textbf{ Hence, the quadrilateral formed by angle bisectors of a cyclic quadrilateral}}$$

$${\textbf{is also cyclic.}}$$

2167323_1162812_ans_c624d803ed544dd2b871622bb3a8f586.PNG

In the diagram above, $$O$$ is the centre of the circle. The value of $$x$$ is

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$$100$$
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$$140$$
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$$150$$
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$$160$$

In the given figure, O is the centre of the circle .What is the value of $$x?$$

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$$115^o$$
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$$125^o$$
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$$155^o$$
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$$230^o$$

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

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$$2\ units$$
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$$p\ units$$
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$$4\ units$$
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$$7\ units$$

Given: In a circle with chords $$AP = BP$$
$$arc\ AP=arc\ PB$$

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True
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False

The sum of the angles in the four segments exterior to a cyclic quadrilateral is equal to $$8$$ right angles.

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True
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False

In the figure ,O is the center of the circle. The value of $$(2a + b + C)$$ in

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$${192^ \circ }$$
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$${180^ \circ }$$
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$${278^ \circ }$$
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$${266^ \circ }$$

In the figure given, $$O$$ is the center of the circle, if $$\angle PAB=108^{o}$$, then find $$\angle BCQ$$.

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$$152^{\circ}$$
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$$120^{\circ}$$
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$$150^{\circ}$$
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$$162^{\circ}$$
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None of these

In the given quadrilateral $$PQRS $$, if $$ \angle RSP = {80}^{0} $$, then $$ \angle RQT= $$ ____.

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$$ {100}^{0} $$
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$$ {80}^{0} $$
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$$ {70}^{0} $$
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$$ {110}^{0} $$

An arc subtends an angle of $$45^{o}$$ in its alternate segment then the angle made by its corresponding major arc is at the centre

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$$270^{o}$$
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$$90^{o}$$
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$$45^{o}$$
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$$315^{o}$$

Look at the given figure having $$ O$$ as the center of the circle and find the value of $$a$$ and $$b$$.

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$$a=55^\circ$$ & $$b=40^\circ$$
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$$a=40^\circ$$ & $$b=55^\circ$$
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$$a=45^\circ$$ & $$b=55^\circ$$
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$$a=40^\circ$$ & $$b=50^\circ$$

BC is the diameter of a circle. Points A and D are situated on the circumference of the semi circle $$\angle$$ABD$$=35^o$$ and $$\angle$$BCD$$=60^o$$, $$\angle$$ADB equal to?

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$$20^o$$
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$$25^o$$
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$$30^o$$
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$$115^o$$

In the given circle, $$AD=BC,\angle BAC={30}^{o}$$ and $$\angle CBD={70}^{o}$$
Find
$$(i)\,\angle BCD$$
$$(ii)\,\angle BCA$$
$$(iii)\,\angle ABC$$
$$(iv)\,\angle ADB$$

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$$(i)\,50^\circ\,(ii)\,80^\circ\,(iii)\,50^\circ\,(iv)\,100^\circ$$
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$$(i)\,80^\circ\,(ii)\,50^\circ\,(iii)\,100^\circ\,(iv)\,50^\circ$$
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$$(i)\,80^\circ\,(ii)\,130^\circ\,(iii)\,100^\circ\,(iv)\,50^\circ$$
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None of these

In the adjoining figure, in $$\triangle OAM \ and \ \triangle OBM$$,
$$ OA = OB $$
$$AM = BM $$
$$OM = OM $$
$$\triangle OAM \ \cong \ \triangle OBM$$
What can you conclude?

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$$\angle OMA = \angle OMB \not= 90$$
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$$\angle OMA = \angle OMB = 90$$
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$$\angle AOB = 90$$
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None of the above

In figure, $$O$$ is the centre of the circle, then

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$$\angle x= \angle y+ \angle z$$
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$$\angle y= \angle x+ \angle z$$
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$$\angle z= \angle x+ \angle y$$
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$$none\ of\ these$$

$$ABCD$$ is a cyclic quadrilateral such that $$\angle ADB=30^{o}$$ and $$\angle DCA=80^{o}$$, then $$\angle DAB=$$?

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$$70^{o}$$
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$$100^{o}$$
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$$150^{o}$$
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$$125^{o}$$

The geometric shape that has no corners is _____.

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square
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circle
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rectangle
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hexagon

State whether following statement is true or false:

The nearer a chord to the centre of a circle, the longer is its length.

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True
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False

Write True or False and justify your answer in each of the following :
ABCD is a cyclic quadrilateral such that $$ \angle $$ A = $$ 90^{\circ} , \angle $$ B = $$ 70^{\circ} , \angle $$ C = $$ 95^{\circ} $$ and $$ \angle $$ D = $$ 105^{\circ} $$.

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True
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False

Four alternative answers for the following question is given. Choose the correct alternative.
In a cyclic quadrilateral $$ \,ABCD$$, twice the measure of $$\angle A$$ is thrice the measure of $$\angle C$$. Find the measure of $$\angle C$$?

0%
$$36$$
0%
$$72$$
0%
$$90$$
0%
$$108$$

CBSE Questions for Class 9 Maths Circles Quiz 8 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Circles Quiz 8 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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