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question_answer1)
In given figure, if chords AB and CD of the circle intersect each other at right angles, then\[x+y=\_\_\_\_.\]
A)
\[{{45}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{75}^{o}}\] done
clear
D)
\[{{90}^{o}}\] done
clear
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question_answer2)
In the given figure, angles subtended by chords AC and BC at the centre O of the circle are \[{{55}^{o}}\] and \[{{155}^{o}}\]respectively. Find\[\angle ACB.\]
A)
\[{{150}^{o}}\] done
clear
B)
\[{{75}^{o}}\] done
clear
C)
\[{{62}^{o}}\] done
clear
D)
\[{{60}^{o}}\] done
clear
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question_answer3)
In the given figure, if PQRS is a cyclic quadrilateral with respective angles. Then, the ratio of\[x\]and y is ____.
A)
1 : 3 done
clear
B)
5 : 6 done
clear
C)
2 : 3 done
clear
D)
None of these done
clear
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question_answer4)
O is the centre of the circle.\[\angle ACB={{40}^{o}}.\]then \[\angle AOB\]is
A)
\[{{50}^{o}}\] done
clear
B)
\[{{80}^{o}}\] done
clear
C)
\[{{90}^{o}}\] done
clear
D)
\[{{40}^{o}}\] done
clear
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question_answer5)
In the given figure, AB = CD = 5 cm OM = 3 cm. Then ON is ____.
A)
4 cm done
clear
B)
6 cm done
clear
C)
1.5 cm done
clear
D)
3 cm done
clear
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question_answer6)
In the given figure; O is the centre of the circle and \[\angle BDC={{42}^{o}}.\]The measure of\[\angle BAC\]is _____.
A)
\[{{42}^{\text{o}}}\] done
clear
B)
\[{{48}^{o}}\] done
clear
C)
\[{{58}^{o}}\] done
clear
D)
\[{{52}^{o}}\] done
clear
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question_answer7)
In the given figure, the value of \[x\]is ____.
A)
\[{{60}^{o}}\] done
clear
B)
\[{{40}^{o}}\] done
clear
C)
\[{{20}^{o}}\] done
clear
D)
None of these done
clear
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question_answer8)
In the given figure,\[\angle ABD={{70}^{o}},\angle ADB={{30}^{o}}.\] Then, \[\angle BCD\]is ____.
A)
\[{{90}^{o}}\] done
clear
B)
\[{{80}^{o}}\] done
clear
C)
\[{{100}^{o}}\] done
clear
D)
\[{{120}^{o}}\] done
clear
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question_answer9)
In the given figure, if \[\angle DAB={{62}^{o}}\]and \[\angle ABD={{58}^{o}},\]then \[\angle ACB\]is equal to _____.
A)
\[{{60}^{o}}\] done
clear
B)
\[{{58}^{o}}\] done
clear
C)
\[{{62}^{o}}\] done
clear
D)
None of these done
clear
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question_answer10)
AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm then the distance of AB from the centre of the circle is ____.
A)
17 cm done
clear
B)
8 cm done
clear
C)
4 cm done
clear
D)
15 cm done
clear
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question_answer11)
In the given figure, \[\angle PQR={{120}^{o}},\]where P, Q and R are points on a circle with centre Then \[\angle OPR\]is ____.
A)
\[{{20}^{o}}\] done
clear
B)
\[{{10}^{o}}\] done
clear
C)
\[{{30}^{o}}\] done
clear
D)
\[{{40}^{o}}\] done
clear
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question_answer12)
PQRS is a cyclic quadrilateral such that PR is a diameter of the circle. If\[\angle QPR={{67}^{o}}\]and \[\angle SPR={{72}^{o}},\]then \[\angle QRS=\_\_\_\_.\]
A)
\[{{41}^{o}}\] done
clear
B)
\[{{23}^{o}}\] done
clear
C)
\[{{67}^{o}}\] done
clear
D)
\[{{18}^{o}}\] done
clear
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question_answer13)
In the given figure, PQRS is a cyclic quadrilateral in which\[PS=RS,\angle SQR=x\]and\[\angle PQS={{60}^{o}}.\]The value of \[x\]is ____.
A)
\[{{30}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{75}^{o}}\] done
clear
D)
\[{{80}^{o}}\] done
clear
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question_answer14)
In the given figure, AB and BC are two chords of the circle with centre O, where\[\angle BAO={{50}^{o}};\]\[\angle BCO={{35}^{o}},\] then \[\angle AOC\]is equal to ____.
A)
\[{{170}^{o}}\] done
clear
B)
\[{{70}^{o}}\] done
clear
C)
\[{{150}^{o}}\] done
clear
D)
None of these done
clear
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question_answer15)
A, B, C and D are four points on a circle. AC and BD intersect at a point E such that \[\angle BEC={{130}^{o}}\]and \[\angle ECD={{20}^{o}},\]then \[\angle BAC\]is ____.
A)
\[{{110}^{o}}\] done
clear
B)
\[{{100}^{o}}\] done
clear
C)
\[{{90}^{o}}\] done
clear
D)
\[{{120}^{o}}\] done
clear
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question_answer16)
ABCD is a cyclic quadrilateral. If\[\angle BCX={{70}^{o}}\]and \[\angle ADX={{80}^{o}}\]then find the values of\[x\]and y respectively.
A)
\[{{70}^{o}},\,\,{{80}^{o}}\] done
clear
B)
\[{{70}^{o}},\,\,{{70}^{o}}\] done
clear
C)
\[{{80}^{o}},\,\,{{80}^{o}}\] done
clear
D)
None of these done
clear
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question_answer17)
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 \[\angle BAC.\]
A)
\[{{45}^{o}}\] done
clear
B)
\[{{58}^{o}}\] done
clear
C)
\[{{60}^{o}}\] done
clear
D)
\[{{40}^{o}}\] done
clear
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question_answer18)
In the given figure, AEDF is a cyclic quadrilateral. The values of \[x\] and y respectively are
A)
\[{{79}^{o}},\,\,{{47}^{o}}\] done
clear
B)
\[{{89}^{o}},\,\,{{37}^{o}}\] done
clear
C)
\[{{89}^{o}},\,\,{{47}^{o}}\] done
clear
D)
\[{{79}^{o}},\,\,{{37}^{o}}\] done
clear
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question_answer19)
O is the centre of the circle having radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. If OA meets BC at P, then OP = ____.
A)
3.6 cm done
clear
B)
1.4 cm done
clear
C)
2 cm done
clear
D)
3 cm done
clear
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question_answer20)
In given figure, if O is the centre of the circle, then \[x\]\[x=\_\_\_\_.\]
A)
\[{{35}^{o}}\] done
clear
B)
\[{{40}^{o}}\] done
clear
C)
\[{{70}^{o}}\] done
clear
D)
\[{{75}^{o}}\] done
clear
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question_answer21)
\[{{C}_{1}}\]is a circle of radius 6 cm,\[{{C}_{2}}\]is a circle I of radius 8 cm. Jyoti wants the two circles to touch tangentially. She knows that there are two possibilities for the distance between their centres. What are these two distances?
A)
3 cm and 4 cm done
clear
B)
2 cm and 8 cm done
clear
C)
2 cm and 14 cm done
clear
D)
6 cm and 8 cm done
clear
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question_answer22)
Fill in the blanks.
[a] P chords subtend equal angles at the centre. |
[b] The arc of a circle subtending a right angle at any point to the circle in the alternating segment is a Q |
[c] The sum of either pair of the opposite angles of a cyclic quadrilateral is R |
A)
B)
C)
D)
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question_answer23)
In the given figure, AOB is the diameter of a circle and CD || AB. If \[\angle BAD={{30}^{o}},\]then \[\angle CAD=\_\_\_\_.\]
A)
\[{{30}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{45}^{o}}\] done
clear
D)
\[{{50}^{o}}\] done
clear
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question_answer24)
State T for true and 'F' for false.
(i) A segment of a circle is the region between an arc and radius of the circle. |
(ii) The line joining the mid point of a chord to the centre of a circle passes through the mid point of the corresponding minor arc. |
(iii) Angles inscribed in the same arc of a circle are equal. |
A)
B)
C)
D)
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question_answer25)
Two circles intersect at two points A and B. If AD and AC are diameters of the circles, then which of the following step is INCORRECT in order to prove that B lies on the line segment DC?
(p) Join AB. |
(q)\[\angle ABC={{90}^{o}}\]and\[\angle ABC={{90}^{o}}\](Angle in semicircle) |
(r)\[\angle ABD+\angle ABC={{360}^{o}}\] |
(s) DBC is a straight line segment. Hence B lies on the line segment DC. |
A)
p done
clear
B)
q done
clear
C)
r done
clear
D)
s done
clear
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