Question 1 :
The _________ of a circle is the distance from the centre to the circumference.
Question 2 :
State whether the following statement are true $(T)$ or false $(F)$.<br>Every chord of a circle is also a diameter.
Question 4 :
Radius of the circle <span>${{\left( x-2 \right)}^{2}}+{{\left( y-3 \right)}^{2}}={{\left( 5\sqrt{5} \right)}^{2}}$ is</span>
Question 5 : Find the radius of the circle given by the equation <div>$2x^2+2y^2+3x+4y+\dfrac{9}{8}=0$.</div>
Question 6 :
A horse is tied to a pole fixed at one corner of $\displaystyle 50m\times 50m$ squate field of grass by means of a 20m long rope. What is the area of that part of the field which the horse can graze?
Question 7 :
What is the minimum radius $(>1)$ of a circle whose circumference is an integer?
Question 8 :
There are two concentric circles. The radii of the two circles are $100\ m$ and $110\ m$ respectively. A wheel of radius $30\ cm$ rolls on the smaller circle and another wheel rolls on the larger circle. After they have completed one revolution, it is found that the two wheels rolled equal number of times on their respective axes. What is the radius of the other wheel?
Question 9 :
If the number of units in the circumference of a circle is same is same as the number of units in the area then the radius of the circle will be
Question 10 :
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 11 :
If $(3, -2)$ is on a circle with center $(-1, 1)$ then the area of the circle is
Question 13 :
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 14 :
The radius of a circular wheel is $1.75\ m$. The number of revolutions that it will make in covering $11\ kms$ is:
Question 15 : <div><span>Line segment joining the centre to any point on the circle is a radius of the circle .</span><br/></div>
Question 16 :
The radius of a wheel is $0.25 m$. How many rounds will it take to complete the distance of $11 km$?
Question 18 :
The length of the diameter of a circle is how many times the radius of the circle
Question 20 :
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 21 :
Sate whether the following statements are true (T) or false (F):<br>Diameter is the longest chord of the circle.
Question 22 :
What is the radius of a circular field whose area is equal to the sum of the areas of three smaller circular fields of radii $12m, 9m$ and $8m$ respectively?
Question 23 :
$AB$ 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 24 :
A roller of diameter 70 cm and length 2m is rolling on the ground What is the area covered by the roller in 50 revolutions?
Question 25 :
If a diameter is drawn it divides the circle into____equal parts
Question 26 :
If 'c' be the circumference and 'd' be the diameter then the value of $ \displaystyle \pi $ is equal to-<br>
Question 27 :
If the circumference of a circle be 8.8 m then its radius is equal to -
Question 29 :
If 9.2 cm is the diameter of a circle then its radius is
Question 30 :
If an arc of a circle subtends an angle of <b></b>$ \displaystyle x^{\circ} $ at the centre then the length of the arc will be equal to - (Given radius of the circle=r)
Question 31 :
If the diameter of a circle is 7 cm, then its radius is<br/>
Question 32 :
The area of circle centred at $(1, 2)$ and passing through $(4, 6)$ is -<br/>
Question 33 :
<span>The circumference of a circular field is $308\:m$ . Find its </span>radius.
Question 34 :
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 35 :
The circumference of a circle is equal to the side of a square whose area measures 407044 sq. cms. What is the area of the circle ?<br>Is it possible to solve this question using digital root method?
Question 37 :
If the area and the circumference of circle are numerically equal, then the radius the circle is ...............
Question 38 :
If $9.2$ cm is the diameter of the circle, then its radius is
Question 39 :
A circular garden has an area of $100\pi$ feet squared. What is the circumference of the garden in feet?
Question 40 :
Distance between two parallel lines is $14$ cm. The radius of circle which will touch the two lines is
Question 41 : 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 42 :
What is the radius of a circle whose circumference is $\pi$?
Question 43 :
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 44 :
If circumference of a circle is $110\ cm$, then its diameter is <br/>
Question 45 :
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 46 :
The abcissae of two points A and B are the roots of the equation $\displaystyle x^{2}+2ax-b^{2}=0 $ and their ordinates are the roots of the equation $\displaystyle x^{2}+2px-q^{2}=0 $. The radius of the circle with AB as diameter is
Question 47 :
When the circumference of a toy balloon is increased from $20\ cm$ to $25\ cm$, the radius is increased by
Question 48 :
If ${ r }_{ 1 },{ r }_{ 2 },$ and ${ r }_{ 3 }$ be the radii of encircles ABC, then $\dfrac { \sum { { r }_{ 1 } } }{ \sqrt { \sum { { r }_{ 1 }{ r }_{ 2 } } } } \\ $is equal to
Question 49 :
State 'T' for true and 'F' for false.<br>(P) Length of ribbon required to cover the semicircular disc of radius $10\ cm$ is $51.4\ cm$.<br>(Q) Ratio of circumference of a circle to its radius is always $2\pi : 1$<br>(R) $500\ m^{2} = 5\ hectares$<br>(S) If $1\ m^{2} = x\ mm^{2}$, then the value of $x$ is $100000$.
Question 50 :
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 51 :
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 52 :
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 53 :
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 54 :
If $\left|n\right|\neq1$, then the locus of a point $P$ is :
Question 55 :
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 56 :
A wheel with a rubber tyre has an outside diameter of $25$cm. When the radius has been decreased a quarter of a centimetre, the number of revolutions of the wheel in one metre will:
Question 57 :
If a bicycle wheel makes $5000$ revolution in moving $11$ km, then diameter of wheel is
Question 58 : 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 59 :
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 60 :
Find the radius of the circle which passes through the origin, $(0, 4)$ and $(4, 0)$.
