Question 2 :
The length of chord of circle with radius 10cm drawn at a distance of 8cm
Question 3 :
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 4 :
The radius of the circle of least size that passes through $(-2, 1)$ and touches both axes is?
Question 5 :
The _________ of a circle is the distance from the centre to the circumference.
Question 7 :
The area of a circle is doubled when its radius $r$ is increased by $n$. Then $r$ equals:
Question 8 :
In a circle with centre O, $OD\bot$ chord AB. If BC is the diameter, then
Question 9 :
Line segment joining the centre to any point on the circle is a radius of the circle.
Question 12 :
Find the radius of a circle whose diameter has endpoints (-3, -2) and (7, 8)
Question 14 :
State whether the following statement are true $(T)$ or false $(F)$.<br/>Two diameters of a circle will necessarily intersect.
Question 16 :
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 17 :
If the radius of a circle is $4\ cm$, then the length of its diameter is
Question 18 :
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 $x$ -<span>axis is :</span>
Question 21 :
Chords AC and BD of a circle intersect each other then the figure ABCD formed will be
Question 22 :
Line segment joining the centre to any point on the circle is
Question 23 :
A chord of a circle, which is twice as long as its radius is
Question 24 :
If the radius of a circle is increased by 3 times then the diameter increases by ____times
Question 25 :
Sate whether the following statements are true (T) or false (F):<br>Diameter is the longest chord of the circle.
Question 26 :
State whether the following statement are true $(T)$ or false $(F)$.<br>Every chord of a circle is also a diameter.
Question 27 :
State whether the following statement are true $(T)$ or false $(F)$.<br/>Every diameter of a circle is also a chord.
Question 28 :
A circle is inscribed in a triangle with sides $8,15 and 17$. The radius of the circle is.
Question 29 :
If $(3, -2)$ is on a circle with center $(-1, 1)$ then the area of the circle is
Question 31 :
The area of the circle centred at $(1,2)$ and passing through $(4,6)$ is
Question 32 : <div>What is the volume in cubic cm of a pyramid whose area of the base is $25 \,sq\,cm$ height $9cm$?</div>
Question 33 : <div><span>The ratio between the diameters of two circles is $ 3: 5$, then find the ratio their </span><span>radii.</span></div>
Question 34 :
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 35 :
If a diameter is drawn it divides the circle into____equal parts
Question 36 :
A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
Question 37 :
Given a circle with centre $O.$ The smallest chord $PQ$ is of length $4$ cm, largest chord $AB$ is of length $10$ cm, and chord $EF$ is of length $7$ cm. Then, the radius of the circle is<br/>
Question 39 :
In a circle with center $O$, a chord $PQ$ is such that $OM\pm PQ$ meeting $PQ$ at $M$. Then
Question 40 :
$AB$ 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 41 :
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 42 :
Sate whether the following statements are true (T) or false (F):<br>The diameter's of a circle are concurrent the centre of the circle is the point common to all diameters.
Question 43 :
Radius of the circle <span>${{\left( x-2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}={{\left( 5\sqrt{5} \right)}^{2}}$ is</span>
Question 44 :
Of all the chords of a circle passing through a given point in it, the smallest is that which<br>
Question 45 :
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 46 :
Sate whether the following statements are true (T) or false (F):<br>The end-point of a diameter of a circle divide the circle into two points, each part is called a semi-circle.
Question 47 :
Find the centre and radius of the circle<br/>$x^2+y^2-4x - 8y -45=0$.
Question 48 : <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 49 :
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 50 :
In a circle of radius $10$ cm, a chord is drawn $6$ cm from the centre. If a chord half the length of the original chord were drawn, its distance in centimeters from the centre would be<br>
Question 51 :
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 52 :
The length of a chord of a circle at a distance of 5 cm from the centre is 24 cm. the diameter of the circle is
Question 53 :
If a chord of the circle ${ x }^{ 2 }+{ y }^{ 2 }=8$ makes equal intercepts of length $a$ on the coordinate axes, then
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 :
$A,B,C$ are three points on a circle such that $AB$ is the chord and $CP$ is the perpendicular to $OP$, where $O$ is the centre and $P$ is any point on $AB$. The radius $r$ of the circle is given by
Question 56 :
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 57 :
If $ax + by - 3 = 0$ is the equation of the shortest chord of the circle $\displaystyle \left ( x-3 \right )^{2}+\left ( y-4 \right )^{2}=4$ passing through the point $(2,3)$, then $|a + b|$ is
Question 58 :
In a circle if a chord $AB$ is nearer to the centre $O$ than the chord $CD$ then:
Question 59 :
What is the radius of the incircle of the right angled triangle whose sides measure $6, 8$ and $10$ units?<br/>
Question 60 :
<span>A tractor driving pulley has its $25 cm$ diameter and revolving at a speed of $960 rpm$. If on the shaft of a thresher, an attached pulley is revolving at a speed of $1600 rpm$. What would be the diameter of this pulley?</span>
Question 61 :
The length of the chord joining the points $(4\cos\theta , 4 \sin\theta )$ and $(4\cos(\theta +60^{\mathrm{o}}))$ ,<br>$(4\sin(\theta +60^{\mathrm{o}}))$ of the circle $x^{2}+y^{2}=16$ is<br>
Question 62 :
The length of the chord of the circle $x^2+y^2+3x+2y-8=0$ intercepted by the y-axis is.<br>
Question 63 :
The line $y=mx+c$ intersect the circle ${ x }^{ 2 }+{ y }^{ 2 }={ r }^{ 2 }$ at the two real distinct points if
Question 64 :
What is the length of the common chord of two circles of radii 15 cm and 20 cm whose centre are 25 cm apart?
Question 65 :
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 66 :
Length of Chord which is at a distance of $3cm$ from the centre of circle of radius $5cm$ is:
Question 67 :
If the length of a chord of a circle is equal to its radius, then find the angle subtended by it at the minor arc of the circle
Question 68 :
Find the centre and radius of the circle.<br>$x^2+y^2-8x + 10y -12=0$
Question 69 :
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 70 : $AB$ is a chord of a circle. Tangent $MC$ touches the circle at $M$ and meets $AB$ produced at $C$. <div>If $MC = 12 cm, AB = xcm$ and $BC= (x-2) cm$ then the value of $x$ is equal to ?</div>
Question 71 :
If the radius of a circle is increased by $4$ times then its diameter increases by
Question 72 :
The area of the circle $x^2 - 2x + y^2 - 10y + k = 0$ is $25\pi$. The value of $k$ is equal to
Question 73 :
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 77 :
If the radius of a circle is increased by 10%, then the corresponding area of new circle wil be.........<br>
Question 78 :
Write True or False: Give reasons for your answers.<br>A circle has only finite number of equal chords.
Question 79 :
Check whether the statement is true or false.<br>Each radius of a circle is also a chord of the circle.<br><br>
Question 80 :
Diameter of a circle is $7.12$ cm, then the radius is
Question 81 :
The condition that the chord $x\cos { \alpha } +y\sin { \alpha } -p =0$ of ${x}^{2}+{y}^{2}-{a}^{2}=0$ may subtend a right angle at the centre of the circle is
Question 82 :
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 83 :
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 84 :
If the radius of the circle is increased by 100%, then the area is increased by
Question 85 :
$PQ$ and $RS$ are two parallel chords of a circle. with centre $C$ such that $PQ=8$ cm and $RS=16$ cm. If the chords are on the same side of the centre and the distance between them is $4$ cm, then the radius of the circle is:<br>
Question 86 :
The length of chord to a circle with radius $10cm$ and distance from center is $8cm$
Question 87 : <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 88 :
The circle of radius $a$ and center at origin $(0,0)$ passes through $(\sqrt3,1)$ find $a$
Question 89 :
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 90 :
Check whether the statement is true or false.<br>Each diameter of a circle is also a chord of the circle.<br>
Question 91 :
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 92 :
If a diameter is drawn in a circle, it divides the circle into____equal parts
Question 93 :
If a chord of the circle ${ x }^{ 2 }+{ y }^{ 2 }=32$ makes equal intercepts of length $l$ on the coordinate axes, then
Question 94 :
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 95 :
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 96 :
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 97 :
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 98 :
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 99 : 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 100 :
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.
