Question 1 :
In a circle, if a chord $AB$ is nearer to the center $O$, then the chord $CD$ is
Question 2 :
A chord of a circle is 12 cm in length and its distance from the centre is 8 cm. Find the length of the chord of the same circle which is at a distance of 6 cm from the centre.
Question 3 : Find the radius of the circle given by the equation <div>$2x^2+2y^2+3x+4y+\dfrac{9}{8}=0$.</div>
Question 4 :
Sate whether the following statements are true (T) or false (F):<br>A diameter of a circle divides the circular region into two parts, each part is called a semi-circular region.
Question 5 :
The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is
Question 6 :
The length of the diameter of a circle is how many times the radius of the circle
Question 7 :
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 10 :
Find the centre and radius of the circle<br/>$x^2+y^2-4x - 8y -45=0$.
Question 11 :
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 13 :
State whether the following statement are true $(T)$ or false $(F)$.<br>Every chord of a circle is also a diameter.
Question 15 :
In a circle with centre O, $OD\bot$ chord AB. If BC is the diameter, then
Question 16 :
$AB$ is a chord of the circle with center $O$ and radius $r$, $OD\pm AB$ meeting $AB$ at $ D$. If $AB =8$ cm and $OD =3$ cm, then $r$ equals
Question 17 :
The measure of perpendicular distance between the biggest chord and the centre of a circle of radius $5$ is
Question 18 :
Sate whether the following statements are true (T) or false (F):<br>A line segment with its end-points lying on a circle is called a diameter of the circle.
Question 19 :
Of all the chords of a circle passing through a given point in it, the smallest is that which<br>
Question 23 :
If 9.2 cm is the diameter of a circle then its radius is
Question 24 :
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 25 :
State whether the following statement are true $(T)$ or false $(F)$.<br/>Two diameters of a circle will necessarily intersect.
Question 26 :
Two chords of lengths 16 cm and 17 cm are drawn perpendicular to each other in circle of radius 10 cm. The distance of their point of intersection from the centre is approximately
Question 27 : <div><span>The ratio between the diameters of two circles is $ 3: 5$, then find the ratio their </span><span>radii.</span></div>
Question 28 :
The point (-4, -2) lies on a circle What is the length of the radius of this circle if the center is located at (-8, -10)?
Question 30 :
If the diameter of a circle decreases to its $\dfrac{1}{4}$ then its radius decreases to
Question 31 :
A circle is inscribed in a triangle with sides $8,15 and 17$. The radius of the circle is.
Question 32 :
A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
Question 33 :
If $(3, -2)$ is on a circle with center $(-1, 1)$ then the area of the circle is
Question 34 :
If $\left( {6, - 3} \right)$ is the one extremity of diameter to the circle ${x^2} + {y^2} - 3x + 8y - 4 = 0$ then its other extremity is -
Question 35 :
<span>The ratio between the diameters of two circles is $3 : 5,$ then find the ratio between their </span>circumferences.<br/>
Question 36 :
Sate whether the following statements are true (T) or false (F):<br>Every circle has unique diameter.
Question 37 :
The area of a circle is doubled when its radius $r$ is increased by $n$. Then $r$ equals:
Question 38 :
What is the radius of the circle with the given diameter $42$ cm?
Question 41 :
The sum of the areas of two circle $A$ and $B$ is equal to the area of a third circle $C$, whose diameter is $30$ cm. If the diameter of circle $A$ is $18$ cm, then the radius of circle B is
Question 42 :
If the number of units in the circumference of a circle is same as the number of units in the area,then the radius of the circle will be<br>
Question 43 :
Find the radius of a circle whose diameter has endpoints (-3, -2) and (7, 8)
Question 44 : <div>What is the volume in cubic cm of a pyramid whose area of the base is $25 \,sq\,cm$ height $9cm$?</div>
Question 45 : <div><span>State the following statement is True or False</span><br/></div>If the radii of the two circles are equal, then the circles are congruent.
Question 46 :
Line segment joining the centre to any point on the circle is a radius of the circle.
Question 47 :
Two circles with centres $A$ and $B$ of radii $3\ cm$ and $4\ cm$, respectively intersect at two points $C$ and $D$ such that $AC$ and $BC$ are tangents to the two circles. Find the 10 times length of the common chord $CD$<br/>
Question 48 :
If a chord of the circle ${ x }^{ 2 }+{ y }^{ 2 }=32$ makes equal intercepts of length $l$ on the coordinate axes, then
Question 49 :
<u></u>The length of the chord cut off by $y = 2x + 1$ from the circle $x^2 + y^2 = 2$ is
Question 50 :
If the radius of the circle is increased by 100%, then the area is increased by
Question 51 :
Length of Chord which is at a distance of $3cm$ from the centre of circle of radius $5cm$ is:
Question 52 :
If PQ is a chord of a circle whose centre is 0 and PR is the tangent to the circle at the point P, then $\angle POQ$ is equal to
Question 53 :
What is the radius of the incircle of the right angled triangle whose sides measure $6, 8$ and $10$ units?<br/>
Question 54 :
Distance between two parallel lines is $14$ cm. The radius of circle which will touch the two lines is
Question 55 :
If $9.2$ cm is the diameter of the circle, then its radius is
Question 56 :
If a diameter is drawn in a circle, it divides the circle into____equal parts
Question 57 :
A straight line $x=y+2$ touches the circle $4(x^2+y^2)=r^2$. The value of $r$ is
Question 58 :
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 59 :
The length of the chord of the circle $x^2+y^2+3x+2y-8=0$ intercepted by the y-axis is.<br>
Question 60 :
The equation of a straight line meeting the circle $\displaystyle x^{2}+y^{2}=100 $ in two points, each point at a distance of 4 from the point $(8, 6)$ on the circle, is
Question 61 :
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 62 :
The point of which the line $9x+y-28=0$ is the chord of contact of the circle $2x^2+2y^2-3x+5y-7=0$ is?
Question 63 :
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 64 :
The radius of the circle which touches $y-$axis at $(0,0)$ and passes through the point $(b,c)$ is
Question 65 :
Diameter of a circle is $7.12$ cm, then the radius is
Question 66 :
The radius of the circle represented by the equations.<br/>$3{x^2}+3y^{2}+\lambda xy+9x+(\lambda -6)y+3=0$ is
Question 67 :
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 68 :
A right angled isosceles triangle is inscribed in the circle $x^2+y^2-4x-2y-4=0$ then length of the side of the triangle is
Question 69 :
If the diameter of a circle is 7 cm, then its radius is<br/>
Question 70 :
If the chord $y=mx+!$ of the circle ${x}^{2}+{y}^{2}=1$ subtend an angle of measure ${45}^{o}$ at the major segment of the circle then value of $m$ is
Question 71 :
Write True or False: Give reasons for your answers.<br>Line segment joining the centre to any point on the circle is a radius of the circle.
Question 72 :
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 73 :
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 74 :
Write True or False: Give reasons for your answers.<br>A circle has only finite number of equal chords.
Question 75 :
The radius of the circle passing through the foci of the ellipse $9x^2 + 16y^2 = 144$ and having its centre at $(0, 3),$ is
Question 76 :
In each of the following, state if the statement is true (T) or false (F):<br>The diameter is twice the radius.
Question 77 :
Find the centre and radius of the circle.<br>$x^2+y^2-8x + 10y -12=0$
Question 78 :
In the circular lawn, there is a $16$ m long path in the form of a chord. If the path is $6$ m away from the centre of the lawn, then the radius of the circular lawn is
Question 79 :
If the area of a circle is equal to sum of the areas of two circles of diameters $10$ cm and $24$ cm, then the diameter of the larger circle (in cm)<span>is:</span>
Question 80 :
If $AB$ and $AC$ are two chords of a circle of radius $5$ cm such that $AB = AC = 4\sqrt 5$ cm, then the length of the chord $BC$ is
Question 81 :
In $\triangle ABC,m\angle B={ 90 }^{ o },AB=4$ and $BC=3$, then the radius of circle touching all three vertices of a triangle will be
Question 82 : If the perimeter of a semi-circular protractor is $66$cm. Find the diameter of the protractor.<div>(Take $\pi=\displaystyle\frac{22}{7}$). </div>
Question 83 :
Assertion: Statement-1: The line $x +9y -12 = 0$ is a chord of contact of a point $P$ with respect to the circle $2x^{2}+ 2y^{2}- 3x +5y -7 = 0$.
Reason: Statement-2: The line joining the points of contacts of the tangents drawn from a point $P$ outside a circle to the circle is the chord of contact of $P $ with respect to the circle.
Question 84 :
Find the length of a chord that is at a distance of $5$ cm form the centre of a circle of radius $13$ cm.
Question 86 :
In a circle if a chord $AB$ is nearer to the centre $O$ than the chord $CD$ then:
Question 87 :
The radius of a circle is $16cm$. The mid point of a chord of the circle lies on the diameter perpendicular to the chord and its distance from the near end of the diameter is $3cm$; If the length of that chord is $m \sqrt{87}$ cm, then the value of $m$ is
Question 88 :
Equation of a straight line meeting the circle $\displaystyle x^{2}+y^{2}=100 $ in two points each point at a distance of $4$ from the point $(8, 6)$ on the circle is
Question 89 :
<span>The circumference of a circle is equal to $72\pi$. Find the radius of this circle.</span>
Question 90 :
The radius of the circle ${ x }^{ 2 }+{ y }^{ 2 }+x+c=0$ passing through the origin is
Question 91 : <p> 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 ?<br/></p>
Question 92 :
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 93 :
Recall that two circles are congruent if they have the small radii. Then the angles subtended by the equal chord to the centres are
Question 94 :
A circle with centre at (2, 4) is such that the line $x+ y + 2 =0$ cuts a chord of length 6. Find the radius of the circle.<br/>
Question 95 :
<span>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</span> length of the chord $AB$ is,
Question 96 :
If $\left|n\right|\neq1$, then the locus of a point $P$ is :
Question 97 :
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 98 :
the length of a chord of a circle $x^2+y^2 =9$ intercepted by the line $x+2y=3$ is
Question 99 :
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 100 : Consider<span><br/>${L}_{1}:2{x}+3{y}+{p}-3=0$<span><br/>${L}_{2}:2{x}+3{y}+{p}+3=0$,<br/><span>where ${p}$ is a real number, and </span></span></span><div><span><span><span>${C}:{x}^{2}+{y}^{2}+6{x}-10{y}+30=0$.<br/><br/><span>STATEMENT 1 : If line $L_{1}$ is a chord of circle $C$, then line $L_{2}$ is not always a diameter of circle $C$.<br/>STATEMENT 2 : If line $L_{1}$ is a diameter of circle $C$, then line $L_{2}$ is not a chord of circle $C$.<br/></span></span></span></span></div>
Question 101 :
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 102 :
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 103 :
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>
Question 104 :
The equation of a chord of the circle $x^2 + y^2 - 3x - 4y - 4=0$, which passes through the origin such that the origin divides it in the ratio $4 : 1$, is
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 106 :
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 107 :
Find the radius of the circle which passes through the origin, $(0, 4)$ and $(4, 0)$.
Question 108 :
A circle touches the $y-$axis at the point $(0,4)$ and cuts the $x-$axis in a chord of length $6$ units. The radius of the circle is
Question 109 :
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 is <span>diameter is</span>
Question 110 :
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 111 :
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 112 :
If one of the diameters of the circle $x ^ { 2 } + y ^ { 2 } - 2 x - 6 y + 6 = 0$ is a chord to the circle with centre $( 2,1 )$ , then the radius of the circle is .
Question 113 :
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 114 :
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
Question 115 :
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 -
