Question 1 :
The tangent to a circle is ..... to the radius through the point of contact.
Question 2 :
A circle and a tangent to the circle have in common
Question 3 :
The two circles ${ x }^{ 2 }+{ y }^{ 2 }={ c }^{ 2 }\left( c>0 \right) $ touch each other if:
Question 4 :
A perpendicular at the end of the radius of a circle is
Question 5 :
Two circle of radii $5.5cm$ and $3.3cm$ respectively touch each other, what is the distance between their centre?
Question 6 :
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 7 :
In a circle with center $O$, a chord $PQ$ is such that $OM\pm PQ$ meeting $PQ$ at $M$. Then
Question 8 : <div>What is the volume in cubic cm of a pyramid whose area of the base is $25 \,sq\,cm$ height $9cm$?</div>
Question 9 :
The length of chord of circle with radius 10cm drawn at a distance of 8cm
Question 10 :
The lengths of tangent drawn from an external point to a circle are equal.
Question 12 :
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 13 :
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 14 : <span>Write true or false :</span><div><br/></div><div>A chord of a circle, which is twice as long as its radius, is a diameter of the circle.</div>
Question 15 :
If ${C}_{1}$ and ${C}_{2}$ and ${r}_{1}$ and ${r}_{2}$ are respectively the centroids and radii of incircles of two congruent triangles, then which one of the following is correct?
Question 16 :
The tangents drawn at the ends of a diameter of a circle are ?
Question 17 :
The common point of a tangent to a circle and the circle is called .....
Question 18 :
A line that intersects a circle at two distinct points is called<br/>
Question 19 :
There are exactly two tangents to a circle passing through a point lying ........ the circle.
Question 20 :
From an external point, if $K$ tangents can be drawn to a circle, then $K$ is equal to <br>
Question 21 :
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 22 :
If the points $\left( {0,0} \right)\,,$ and $\left( {2,0} \right)\,,$ are concyclic then K=
Question 23 :
What is the length of shortest path by which one can go from $(-2,0)$ to $(2,0)$ without entering the interior of circle, ${ x }^{ 2 }+{ y }^{ 2 }=1$?
Question 24 :
A square is inscribed in the circle $x^{2} + y^{2} -2x + 4y -93 = 0$ with its sides parallel to the axes of coordinates. The coordinates of the vertices are
Question 25 :
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 26 :
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 27 :
Tangents are drawn to the curve $y=\sin { x } $ from the origin. The point of contact lie on
Question 29 :
The equation of the circle of the radius $2\sqrt{2}$ whose centre lies on the line $x-y=0$ and which touches the line $x+y=4$, and whose centre's coordinates satisfy the inequality $x+y>4$ is
Question 30 :
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 31 :
Tangents PA and PB drawn to $x^2+y^2=9$ from any arbitrary point 'P' on the line $x+y=25$. Locus of midpoint of chord AB is<br>
Question 32 :
A wheel of radius $8$ units rolls along the diameter of a semicircle of radius $25$ units; it bumps into this semicircle. What is the length of the portion of the diameter that cannot be touched by the wheel?
Question 33 :
Equation of pair of tangents from $(0,1)$ on circle $x^{2}+y^{2}=\dfrac {1}{4}$ , is
Question 35 :
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 36 :
The circles whose equations are ${ x }^{ 2 }+{ y }^{ 2 }+{ c }^{ 2 }=2ax$ and ${ x }^{ 2 }+{ y }^{ 2 }+{ c }^{ 2 }-2by=0$ will touch each other externally if
Question 37 :
A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is:
Question 38 :
For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement amongst the following is
Question 39 :
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 40 :
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>
