Question 1 :
$AB$ 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 2 :
If the area of the circle $x^2 + y^2 + 4x + 2y + k = 0$ is $5\pi $ square $cms$ then $k =$
Question 5 :
Centre of the circle $x^2 + y^2 - 2x + 4y + 1 = 0$ is-
Question 6 :
The circumference of a circle is $100$ inches. The side of a square inscribed in this circle, expressed in inches, is:
Question 7 :
If a diameter is drawn it divides the circle into____equal parts
Question 8 :
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 9 :
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 10 :
If a chord of length $2\sqrt { 2 }$ subtends a right angle at the centre of the circle, then its radius is
Question 11 :
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 12 :
A circle is inscribed in a triangle with sides $8,15 and 17$. The radius of the circle is.
Question 13 :
The length of the diameter of a circle is how many times the radius of the circle 
Question 14 :
Find the circumference of the circles with the radius 7cm :(Take $\pi =\dfrac{22}{7}$) 
Question 15 :
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 16 :
State true or false:<br/>Line segment joining the centre to any point on the circle is a radius of the circle.
Question 17 :
The diameter of the circle is $2$ cm. What is the circumference?<br/>
Question 19 :
One angle of a cyclic trapezium is double the other. What is the measure of the larger angle?
Question 20 :
At the centre of circle, opposite sides of a quadrilateral circumscribing a subtend 
Question 21 :
In a circle with centre O, $OD\bot$chord AB. If BC is the diameter, then
Question 22 :
The area of a circle is doubled when its radius $r$ is increased by $n$. Then $r$ equals:
Question 23 :
If a line intersects a circle in two distinct points then it is known as a
Question 24 :
Chords AC and BD of a circle intersect each other then the figure ABCD formed will be
Question 25 :
Of all the chords of a circle passing through a given point in it, the smallest is that which<br>
Question 26 :
In a triangle $ABC, a : b : c =4 : 5 : 6$. The ratio of radius of circum to the incircle
Question 27 :
The circumcircle of the triangle whose sides are<br>${L}_{1}=3x+y-5=0 , {L}_{2}=2x+y-3=0 , {L}_{3}=3x+2y-7=0$ is
Question 28 :
Assertion: If the centroid of an equilateral triangle is $(2,2)$ and its one vertex is $(-3,4)$, then the equation of its circumcircle is ${ x }^{ 2 }+{ y }^{ 2 }-4x-4y-21=0$
Reason: Circumcircle coincides with the centroid of an equilateral triangle.
Question 29 :
If tangents $QR, PR, PQ$ and drawn respectively at $A, B, C$ to the circle circumscribing an acute-angled $\Delta ABC$, so as the form anther $\Delta PQR$, then the $\angle RPQ$ is equal to -
Question 30 :
If one angle of cyclic quadrilateral is $70^o$, then the angle opposite to it is.
Question 31 :
In triangle $ABC$, let $AD, BE$ and $CF$ be the internal angle bisectors with $D, E$ and $F$ on the sides $BC, CA$ and $AB$ respectively. Suppose $AD, BE$ and $CF$ concur at $I$ and $B, D, I, F$ are concyclic, then $\angle$IFD has measure:<br/>
Question 32 :
In a cyclic quadrilateral ABCD, $\angle A=5x, \angle C=4x$ the value of x is
Question 33 :
Assertion: If in a cylic quadrilateral, one angle is $40^0$, then the opposite angle is $140^0$
Reason: Sum of opposite angles in a cyclic quadrilateral is equal to $360^0$
Question 34 :
$(\sqrt{29}, 0), (5, 2), (2, -5), (-1, \mathrm{k})$ and $(\mathrm{k}\neq 0)$ are concyclic, then $k=$<br/>
Question 35 :
Quadilateral ABCD is cyclic. If $m \angle B = 60$ then $m \angle D = $_____________
Question 36 :
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 37 :
If ABCD is acyclicquadrilateral,<b>$\tan B - \tan D =2\sqrt { 3 }$ then $\tan 3 B =$</b>
Question 38 :
If $ABCD$ is a cyclic quadrilateral, then find which of the following statements is not correct.
Question 39 :
In a cyclic quadrilateral $ABDC,\,\angle CAB=80^{\circ}$ and $\angle ABC=40^{\circ}$. The measure of the $\angle ADB$ will be
Question 40 :
If $\Box ABCD$ is a cyclic quadrilateral, then find which of the following statement is not correct?<br/>
Question 41 :
Four alternative answers for the following question is given. Choose the correct alternative.<br>In a cyclic $\Box \,ABCD$, twice the measure of $\angle A$ is thrice the measure of $\angle C$. Find the measure of $\angle C$?
Question 42 :
If lines $x-2y+3=0$, $3x+ky+7=0$ cut the coordinate axes in concyclic points, then $k=?$
Question 43 :
$\Box ABCD$ is a cyclic quadrilateral, then the angles of the quadrilateral in the same order are:
Question 44 :
Write True or False and justify your answer in each of the following :<br>ABCD is a cyclic quadrilateral such that $ \angle $ A = $ 90^{\circ} , \angle $ B = $ 70^{\circ} , \angle $ C = $ 95^{\circ} $ and $ \angle $ D = $ 105^{\circ} $.
Question 45 :
Is the area of the largest circle that can be drawn inside a rectangle of length a cm and breadth b cm $(a > b)$ is $\pi b^2 \,cm^2$ ? why ?
Question 46 :
If a circle passes through the points of intersection of the coordinate axes with the lines $\lambda x - y + 1 = 0$ and $x - 2y + 3 = 0$, then the value of $\lambda$ is
Question 47 :
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 48 :
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 49 :
I. If the points $(\mathrm{a},0)$ , $(\mathrm{b},0)$ , $(0,\mathrm{c})$ , $(0,\mathrm{d})$ are concyclic, then $ab=cd$<br/>II. If the points $(1,-6) , (5,2), (7,0), (-1, \mathrm{k})$ are concyclic then $\mathrm{k}=-3$.<br/>
Question 50 :
If two lines $\displaystyle \displaystyle a_{1}x+b_{1}y+c_{1}=0$ and $\displaystyle a_{2}x+b_{2}y+c_{2}=0$ cut the coordinate axes in concyclic points,then <br>
Question 51 :
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 52 :
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 53 :
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 54 :
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 55 :
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 56 :
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 57 :
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 59 :
$A$ 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 60 :
the length of a chord of a circle $x^2+y^2 =9$ intercepted by the line $x+2y=3$ is
Question 61 :
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 62 :
$\mathrm{P} (\sqrt{2}, \sqrt{2})$ 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 63 :
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 64 :
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 65 :
If the points $\left( {0,0} \right)\,,$ and $\left( {2,0} \right)\,,$ are concyclic then K=
Question 66 :
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 67 :
$\triangle ABC$ 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 68 :
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 69 :
Find the radius of the circle which passes through the origin, $(0, 4)$ and $(4, 0)$.
Question 70 :
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 71 : <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 72 :
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 73 :
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 74 :
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 75 :
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 76 :
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 77 :
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 78 :
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 79 :
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
