Question 2 :
If a circle passing through the point $( - 1,0 )$ touches $y$-axis at $( 0,2 )$ then the length of the chord of the circle along the $x$ -axis is :
Question 3 :
There are $15$ radial spokes in a wheel, all equally inclined to one another. Then there are two spokes which
Question 4 :
Write true or false :<br/>A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
Question 7 :
The radius of the circle of least size that passes through $(-2, 1)$ and touches both axes is?
Question 8 :
The radius and length of an arc of a circle are 35 cm and 22 cm respectively The angle subtended by the arc at the centre of the circle is
Question 9 :
A circle of radius $25$ units has a chord going through a point that is located $10$ units from the centre. What is the shortest possible length that chord could have ?
Question 10 :
Coordinates of the centre of the circle which bisects the circumferences of the circles $x^{2}+y^{2}=1:\x^{2}+y^{2}+2x-3=0$ and $x^{2}+y^{2}+2y-3=0$ is
Question 11 :
If a chord of length $2\sqrt { 2 }$ subtends a right angle at the centre of the circle, then its radius is
Question 12 :
If the radius of a circle is increased by 3 times then the diameter increases by ____times
Question 13 :
The ratio between the diameters of two circles is $3 : 5,$ then find the ratio between their circumferences.<br/>
Question 14 :
If $(3, -2)$ is on a circle with center $(-1, 1)$ then the area of the circle is
Question 15 :
If a line intersects a circle in two distinct points then it is known as a
Question 16 :
Consider the following statements and identify which are correct:<br>i) A secant to a circle can act as a chord.<br>ii) A chord cannot be a secant to the circle.<br>
Question 17 :
$\Box ABCD$ is a Rhombus. If it is inscribed in $\odot \left( 0,r \right) $, then $\Box ABCD$ is a ..............
Question 18 :
The minute hand ofa clock is 14 cm long. How much distance does the end of the minute handtravel in 15 minutes? $\displaystyle\left(Take\:\pi=\frac{22}{7}\right)$
Question 19 :
In a circle with centre O, $OD\bot$chord AB. If BC is the diameter, then
Question 20 :
Find the circumference of the circles with the radius 7cm :(Take $\pi =\dfrac{22}{7}$) 
Question 21 :
If the line $hx + ky = 1$ touches $x^2 + y^2 = a^2$, then the locus of the point (h, k) is a circle of radius
Question 22 :
From a point $A$, the length of a tangent to a circle is $24$ cm and the distance of $A$ from the center is $25$ cm. The radius of the circle is
Question 23 :
Of all the chords of a circle passing through a given point in it, the smallest is that which<br>
Question 24 :
The center of a circle represented by the equation$\displaystyle \left ( x-2 \right )^{2}+\left ( y+3 \right )^{2}=100$ is located in Quadrant _____
Question 25 :
If $(x, 3)$ and $(3, 5)$ are the extremities of a diameter of a circle with centre at $(2, y)$, then the value of $x$ and $y$ are <br/>
Question 26 :
A wire is in the form of a circle of radius-28 cm, then the side of the square into which it can be bent is<br>
Question 29 :
In a circle of diameter 10 cm, the length of each of 2 equal and parallel chords is 8 cm, then the distance between these two chords is
Question 31 :
A line that intersects a circle at two distinct points is called<br/>
Question 33 :
Draw a circle and any two of its diameters. If you join the ends of these diameters, and if the diameters are perpendicular to each other the figure formed is a Rhombus
Question 34 :
Chords AC and BD of a circle intersect each other then the figure ABCD formed will be
Question 36 :
Radius of the circle ${{\left( x-2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}={{\left( 5\sqrt{5} \right)}^{2}}$  is
Question 37 :
What are the coordinates of the center of this circle?<br>$\displaystyle x^{2}+\left ( y+7 \right )^{2}=11$<br>
Question 40 :
What is the volume in cubic cm of a pyramid whose area of the base is $25 \,sq\,cm$ height $9cm$?
Question 42 :
A circle has two equal chords AB and AC. Chord AD cuts BC in E. If $AC=12\:cm$ and $AE=8\:cm$,then AD is equal to
Question 43 :
The _________ of a circle is the distance from the centre to the circumference.
Question 44 :
ACB is tangent to a circle at C. CD and CE are chords such that $\angle ACE > \angleACD$. If $\angle ACD = \angle BCE = 50^{\circ}$, then which is correct answer?
Question 45 :
If a diameter is drawn it divides the circle into____equal parts
Question 46 :
Say true or false.<br>The centre of a circle is always in its interior.<br>
Question 48 :
The Chord of contact of tangents from a point $P$ to a circle passes through $Q$. If $l_1$ and $l_2$ are the lengths of the tangents from $P$ and$Q$ to the circle, then$PQ$ is equal to
Question 49 :
The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is
Question 51 :
If the line $3x-4y-8=0$ divides the circumference of the circle with centre $(2,-3)$ in the ratio $1:2$. Then, the radius of the circle is
Question 52 :
If the lines ${ a }_{ 1 }x+{ b }_{ 1 }y+{ c }_{ 1 }=0$ and ${ a }_{ 2 }x+{ b }_{ 2 }y+{ c }_{ 2 }=0$ cuts the coordinate axes in concyclic points, then
Question 53 :
A regular hexagon & a regular dodecagon are inscribed in the same circle. If the side of the dodecagon is $(\sqrt{3} -1)$, then the side of the hexagon is
Question 54 :
If two chords of the circle ${ x }^{ 2 }+{ y }^{ 2 }-ax-by=0$, drawn from the point $\left( a,b \right)$ is divided by the x-axis in the ratio $2:1$ then:
Question 55 :
Let a circle passing through $(4, 0)$ touches the circle ${ x }^{ 2 }+{ y }^{ 2 }+4x-6y-12=0$, then radius of circle $C$ is 
Question 56 :
If the radius of the circle is increased by 100%,then the area is increased by
Question 57 :
If $OA$ and $OB$ are two equal chords of the circle $x^{2} + y^{2} -2x + 4y = 0$ perpendicular to each other and passing through the origin $O$, the slopes of $OA$ and $OB$ are the roots of the equation
Question 58 :
In a circle of radius $7$ cm, an arc subtends an angle of $\displaystyle 108^{\circ} $ at the centre. The area of the sector is $\displaystyle \left ( \pi =\frac{22}{7} \right )$
Question 59 :
In a cyclic quadrilateral $ABDC,\,\angle CAB=80^{\circ}$ and $\angle ABC=40^{\circ}$. The measure of the $\angle ADB$ will be
Question 60 :
If a circle passes through the points of intersection of the lines $x-2y+3=0$ and$\lambda x-y+1=0$ with the axes of reference then the value of$\lambda $ is
Question 61 :
If $\displaystyle A=(5,8), $ then area of $ \displaystyle \triangle ABD $ in square units is<br>
Question 62 :
If the radius of a circle is increased by 10%, then the corresponding area of new circle wil be.........<br>
Question 63 :
What are the coordinates of the center of this circle?<br>$\displaystyle \left ( x+3 \right )^{2}+\left ( y-5 \right )^{2}=16$<br>
Question 64 :
The equation of the chord of the circle $x ^ { 2 } + y ^ { 2 } - 6 x + 8 y = 0$ which is bisected at the point $( 5 , - 3 ) ,$ is
Question 65 :
If $ABCD$ is a cyclic quadrilateral, then find which of the following statements is not correct.
Question 66 :
Find the radius of the circle passing through the point $(2, 6)$ two of whose diameters are $x+y=6$ and $x+2y=4$
Question 67 :
The internal centre of similitude of two circles ${ \left( x-3 \right) }^{ 2 }+{ \left( y-2 \right) }^{ 2 }=9,{ \left( x+5 \right) }^{ 2 }+{ \left( y+6 \right) }^{ 2 }=9$ is
Question 68 :
$AB$ is a diameter of a circle and $C$ is any point on the circumference of the circle. Then
Question 69 :
If the tangent $PQ$ and $PR$ are drawn to the circle ${ x }^{ 2 }+{ y }^{ 2 }={ a }^{ 2 }$ from the point $P\left( { x }_{ 1 },{ y }_{ 1 } \right) $, then the equation of the circumcircle of $\triangle PQR$ is 
Question 70 : The table shown here contains co-ordinates for two endpoints of a circle's diameter Which of these points is the center of the circle ?<table class="wysiwyg-table"><tbody><tr><td>x</td><td>y</td></tr><tr><td>2</td><td>5</td></tr><tr><td>-2</td><td>5</td></tr></tbody></table>
Question 71 :
If a straight line through $C(-\sqrt{8}, \sqrt{8})$ making an angle $135^o$ with the axes and cuts the circle $x=5\cos\theta$. $y=5\sin\theta$ in points A and B then AB$=?$
Question 72 :
The area of circle centred at $(1, 2)$ and passing through $(4, 6)$ is -<br/>
Question 73 :
In a circle with centre $O$, two unequal chords $PQ$ and $RS$ intersect each other at $M$, then $\Delta PMR$ and $\Delta QMS$ are
Question 74 :
The common chord of $x^{2}+y^{2}-4x-4y=0$ and $x^{2}+y^{2}=16$ subtends at the origin an angle to
Question 75 :
If $\Box ABCD$ is a cyclic quadrilateral, then find which of the following statement is not correct?<br/>
Question 76 :
Consider the circle $S: x^2 + y^2 - 4x - 1 = 0$ and the line $L : y = 3x - 1$. If the line $1$ cuts the circle at $A$ & $B$, then the length of the chord $AB$ is,
Question 77 :
Find the centre and radius of the circle.<br>$x^2+y^2-8x + 10y -12=0$
Question 78 :
Write True or False and justify your answer in each of the following :<br/>If a number of circles touch a given line segment PQ at a point A,  then their  centres lie on the perpendicular bisector of PQ.<br/>
Question 79 :
Write True or False and justify your answer: <br/>Two chords AB and AC of a circle with center O are on the opposite sides of OA . Then $ \angle $ OAB = $ \angle $ OAC .
Question 80 :
$(\sqrt{29}, 0), (5, 2), (2, -5), (-1, \mathrm{k})$ and $(\mathrm{k}\neq 0)$ are concyclic, then $k=$<br/>
Question 81 :
On the circle with center O,points A,B are such that OA=AB . A point C is located on the tangent at B to the circle such that A and C are on the opposite side of the line OB and AB =BC.The segment AC intersects the circle again at F.Then the ratio $\angle BOF :\angle BOC$ is equal to :
Question 82 :
If $y=2x+K$ is a diameter to the circle $2(x^{2}+y^{2})+3x+4y-1=0$, then $K$ equals
Question 83 :
If the chord $y=mx+1$ of the circle ${x}^{2}+{y}^{2}=1$ subtends an angle of measure ${45}^{o}$ at the major segment of the circle then the value of $m$ is
Question 84 :
If a chord of the circle ${ x }^{ 2 }+{ y }^{ 2 }=32$ makes equal intercepts of length $l$ on the coordinate axes, then $\left| l \right| <$
Question 85 :
Write True or False and justify your answer: <br/>Two chords AB and CD of a circle are each at distances $ 4\,cm $ from the center. Then AB = CD .
Question 86 :
If the lengths of the chords intercepted by the circle ${x}^{2}+{y}^{2}+2gx+2fy=0$ from the coordinate axes are $10$ and $24$ units, respectively, then the radius of the circle is
Question 87 :
Calculate the radius of the circle, if it has a circumference of $16\pi$ feet. 
Question 88 :
A chord $AB$ drawn from the point $A(0,3)$ at circle $x^2+4x+(y-3)^{2}=0$ and it meets to $M$ in such a way that $AM=2AB$, then the locus of point $M$ will be<br/>
Question 90 :
Let a circle be given by $2x\left( x-a \right) +y\left( 2y-b \right) =0\left( a\neq 0,b\neq 0 \right) $. If two chords, each bisected by the x-axis, can be drawn to the circle from $\displaystyle \left( a,\frac { b }{ 2 }  \right) $, then 
Question 91 :
If $9.2$ cm is the diameter of the circle, then its radius is
Question 92 : <p>The length of common chords of circles $x^2+y^2+px=0$ and $x^2+y^2+gy=0$ is</p>
Question 93 :
From a point inside the circle how many secants can be drawn to the circle?
Question 94 :
The radius of the circle, which is touched by the line $y=x$ and has its centre on the positive direction of x-axis and also cuts-off a chord of length $2$ units along the line $\sqrt { 3 } y-x=0$, is
Question 95 :
If ABCD is acyclicquadrilateral,<b>$\tan B - \tan D =2\sqrt { 3 }$ then $\tan 3 B =$</b>
Question 96 :
In a cyclic quadrilateral ABCD, $\angle A=5x, \angle C=4x$ the value of x is
Question 97 :
$O$ is the centre of a circle with radius $5$ cm. $LM$ is the diameter of the circle. $P$ is a point on the plane of the circle such that $LP=6$ cm and $MP=8$ cm. Then $P$ lies.<br>
Question 98 :
The length of the chord of circle $x^{2}+y^{2}-6x-16=0$ which is at a distance of $3cm$ from center 
Question 99 :
The equation of the circle circumscribing the triangle formed by the lines $x+y=6$, $2x+y=4$ and $x+2y=5$ is:
Question 100 :
The distance between the chords of contact of tangents to the circle $x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$ from the origin and from the point $( g , f )$ is<br/>
Question 101 :
$\mathrm{P} (\sqrt{2}, \sqrt{2})$ is a point on the circle $\mathrm{x}^{2}+\mathrm{y}^{2}=4$ and $\mathrm{Q}$ is another point on the circle such that arc $\displaystyle \mathrm{P}\mathrm{Q}=\frac{1}{4}$ (circumference). The coordinates of $\mathrm{Q}$ are<br>
Question 102 :
If the curves $ax^2+4xy+2y^2+x+y+5=0$ and $ax^2+6xy+5y^2+2x+3y+8=0$ intersect at four concyclic points then the value of $a$ is 
Question 103 :
Each of the height and radius of the base of a right circular cone is increased by $100$%. The volume of the cone will be increased by
Question 104 :
Read the statements given and identify the correct option.<br>(i) Every diameter of a circle is also a chord.<br>(ii) Every chord of a circle is also a diameter.<br>(iii) The centre of a circle is always in its interior.<br>
Question 105 :
If the tangents $PQ$ and $PR$ are drawn to the circle ${ x }^{ 2 }+{ y }^{ 2 }={ a }^{ 2 }$ from the point $P\left( { x }_{ 1 },{ y }_{ 1 } \right) $, then the equation of the circumcircle of $\triangle PQR$.
Question 107 :
A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to
Question 108 :
Consider a family of circles passing through the points $\left(3,7\right)$ and $\left(6,5\right)$. The chords in which the circle ${x}^{2}+{y}^{2}-4x-6y-3=0$ cuts the family of circles are concurrent at the point
Question 109 :
A bug travels all the way around a circular path in $30$ minutes travelling at $62.84$ inches per hour. What is the radius of the circular path?
Question 110 :
A chord AB of a circle subtends an angle $\theta$ at a point C on the circumference, $\triangle ABC$ has the maximum area when
Question 111 :
The radius of a circle with center$\left( {a,b} \right)$ and passing through the center of the circle${x^2} + {y^2} - 2gx + {f^2} = 0$ is -
Question 112 :
$A$ circle $C$ of radius $1$ is inscribed in an equilateral triangle $PQR$. The points of contact of <br/>$C$ with the sides $PQ,QR, RP$ are $ D, E, F $ respectively. The line $PQ$ is given by the equation <br/>$\sqrt {3} x + y -6 = 0 $ and the point $D$ is $\left(\dfrac {\sqrt{3} }2, \dfrac 32\right)$. Further it is given that the origin <br/>and the centre of $C$ are on the same side of $PQ.$ Points $E$ and $F$ are given by<br/>
Question 113 :
If OA and OB are equal perpendicular chords of the circles $x^2 + y^2 - 2x + 4y = 0$, then equation of OA and OB are where O is origin.
Question 114 :
The locus of the foot of the perpendicular from the origin to chords of the circle $\mathrm{x}^{2}+\mathrm{y}^{2}-4\mathrm{x}-6\mathrm{y}-3=0$ which substend a right angle at the origin, is<br>
Question 115 :
If $\left( \alpha ,\beta  \right) $ is a point on the chord $PQ$ of the circle ${ x }^{ 2 }+{ y }^{ 2 }=19,$ where the coordinate of $P$ and $Q$ are $(3,-4)$ and $(4,3)$ respectively, then
Question 116 :
If a chords of the circle $\displaystyle x^{2}+y^{2}=8$ makes equal intercepts of length a on the coordinate axis then a can be<br>
Question 117 : <p>Suppose $2016$ points of the circumference of a circle points are coloured red and the remaining points are coloured blue. Find the minimum possible value of a natural number $n$, for which there exists a regular $n$- sided polygon whose all vertices are blue.</p>
Question 118 :
The equation of the circle and its chord are respectively $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ are $xcos \alpha + y \sin \alpha = p.$ The equation of the circle of which this chord isdiameter is
Question 119 :
Find the radius of the circle which passes through the origin, $(0, 4)$ and $(4, 0)$.
Question 120 :
If in a $\triangle ABC, A = (2, 20), circumcentre = (-1, 2)$ and orthocenter $= (1, 4)$, then the coordinates of mid point of side opposite to vertex $A$ is
Question 121 :
P and Q are two points on a circle of centre C and radius $\displaystyle \alpha$ the angle PCQ being $\displaystyle 2\theta$ then the length of PQ is 
Question 122 :
Chord is drawn to the circle $\displaystyle x^{2}+y^{2}-4x-2y=0$ at a point where it cuts the x-axis whose slope is parallel to the tangent at an origin. The intercept of the chord on y-axis is
Question 123 :
If the points $\left( {0,0} \right)\,,$ and $\left( {2,0} \right)\,,$ are concyclic then K=
Question 124 :
$\triangle ABC$ is inscribed in a circle. Point $P$ lies on the circle between $A$ and $C$. If $m(\text{arc}\, APC) = 60^\circ$ and $\angle BAC = 80^\circ$, find $m\angle ABC.$
Question 125 :
A chord of length $16$ cm is drawn in a circle at a distance of $15$ cm from its center. Find the radius of the circle.<br/>
Question 126 :
Let  $a$  and  $b$  represent the length of a right triangle's legs. If  $d $ is the diameter of a circle inscribed into the triangle and $ D$  is the diameter of a circle circumscribed on the triangle, then  $d + D$  equals
Question 127 :
The inner circumference of a circular track is $24\pi$m. The track is $2$m wide from everywhere. The quantity of wire required to surround the path completely is _________.
Question 128 :
the length of a chord of a circle $x^2+y^2 =9$ intercepted by the line $x+2y=3$ is
Question 129 :
The coordinates of the middle point of the chord cut-off by $2x - 5y +18 = 0$ by the circle<br>$x^2 + y^2 - 6x + 2y - 54 = 0$ are<br>
