Circles

Q.

The number of ways in which $5$ ladies and $7$ gentlemen can be seated in a round table so that no two ladies sit together, is equal to:

1. $\frac{7}{2}{\left(720\right)}^2$

2. $7{\left(360\right)}^2$

3. $7{\left(720\right)}^2$

4. $720$

5. $360$

Q. In the given figure, AB is chord of the circle with centre O, BT is tangent to the circle. The values of x and y are

1. ${52}^{\circ },{52}^{\circ }$
2. ${58}^{\circ },{52}^{\circ }$
3. ${60}^{\circ },{64}^{\circ }$
4. ${58}^{\circ },{58}^{\circ }$

Q. ABC is a right angled triangle, AB = 3cm, BC = 5 cm and AC = 4cm, then the inradius of the circle is:

1. 1 cm
2. 1.25 cm
3. 1.5 cm
4. None of these

Q.

Two mutually perpendicular chords AB and CD meet at a point P inside the circle such that AP=6 units PB=4 units and DP=3 units. What is the area of the circle?

1. 
   

2. 
   

3. 
   

4. 
   

Q.

Let $ABCD$ be a square of the side of unit length. Let a circle $C_1$ centered at $A$ with a unit radius is drawn. Another circle $C_2$ which touches $C_1$ and the lines $AD$ and $AB$ is tangent to it, is also drawn. Let a tangent line from point $C$ to the circle $C_2$ meet the side$AB$ at $E$. If the length of $EB$ is $ɑ+\sqrt{3}\beta$, where $ɑ,\beta$ are integers, then $ɑ+\beta$ is equal to ___

Q. O and O' are the centres of circle of radii 20 cm and 37 cm. AB = 24 cm. What is the distance OO'?

1. 51 cm
2. 48 cm
3. 45 cm
4. 35 cm

Q.

ABCD is a quadrilateral inscribed in a circle with centre O. If $\angle COD=120$ degrees and $\angle BAC=30$ degrees, then the value of $\angle BCD$ ( in degrees) is ___

Q. A smaller circle touches internally to a larger circle at A and passes through the centre of the larger circle. O is the centre of the larger circle and BA, OA are the diameters of the larger and smaller circles respectively. Chord AC intersects the smaller circle at a point D. If AC = 12 cm, then AD is:

1. 4 cm
2. Data insufficient
3. 6 cm
4. 5.6 cm

Q.

Three circles, each of radius 20 and centres at P, Q, R. Further, AB= 5, CD= 10 and EF= 12. What is the perimeter of the triangle PQR?

1. 66

2. 93

3. 120

4. 87

Q. A ladder is placed so as to reach a window 63 cm above the foot of the ladder. The ladder is then turned over to the opposite side of the street and is found to reach a point 56 cm high. If the ladder is 65 cm long, then the width of the street is ____.

1. 59 cm
2. 39 cm
3. 49 cm
4. 29 cm
5. None of these

Q. In the adjoining figure $\angle ACE$ is a right angle there are three circles which just touch each other and AC and EC are the tangents to all the three circles. What is the ratio of radii of the largest circle to that of the smallest circle ?

1. $Noneoftheabove$
2. $17:12\sqrt{2}$
3. $1:(17-12\sqrt{2})$
4. $12:17\sqrt{2}$

Q.

A line is drawn through the point $P(3,11)$ to cut the circle $x^2+y^2=9$ at $AandB$. Then $PA\mathit{.}PB$ is equal to

1. $9$

2. $121$

3. $205$

4. $139$

Q.

An isosceles triangle is inscribed in a circle such that one of its sides is the diameter of the circle. Find the measure of the side of the triangle(other than diameter) if the radius of the circle is 8 m.

1. 16 m

2. 8 m

3. 16 m

4. m

Q.

A circle of radius 3 crosses the centre of a square of side length 2. Find the approximate positive difference between the areas of the non-overlapping portions of the figures.

1. 22

2. 26

3. 24

4. cannot be determined

Q. What is the distance between the points of tangency of a common tangent AB to two circles I and II which are externally tangent to each other. The radii of the two circles are 9 and 16 units.

1. 24

2. 22

3. 27

4. 17√3

Q. A trapezium PQRS inscribes a circle which touches the circle at M, A, N, B, Radius of the circle is 10 cm. The length of each non-parallel side is 21 cm. What is the perimeter of trapezium?

1. 82 cm
2. 84 cm
3. 85.5 cm
4. Can't be determined

Q. In the given figure, PQ is the tangent of the circle. Line segment PR intersects the circle at N and R. PQ = 15 cm, PR = 25 cm, find PN:

1. 15 cm
2. 10 cm
3. 9 cm
4. 6 cm

Q.

A square and an equilateral triangle are drawn on the same base. The ratio of their areas is -

1. 1: 2

2. 4:√3

3. √3:4

4. 1: 1

5. 4:1

Q. The radius of a circle is 20cm. The radii (in cm) of three concentric circles drawn in such a manner that the whole area is divided into four equal parts, are:

1. $\frac{10\sqrt{3}}{3},\frac{10\sqrt{2}}{3},\frac{10}{3}$
2. $20\sqrt{2},20\sqrt{3},20$
3. $10\sqrt{3},10\sqrt{2},10$
4. 17, 14, 9

Q. In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If $\angle$ATC = 30${}^{\circ }$ and $\angle$ACT = 50${}^{\circ }$, then the $\angle$BOA is :
(CAT 2003)

1. 80°
2. not possible to determine
3. 100°
4. 150°

Q. In the given figure, CD is a direct common tangent to two circles intersecting each other at A and B, then $\angle CAD+\angle CBD=$?

1. ${120}^{\circ }$
2. ${180}^{\circ }$
3. ${90}^{\circ }$
4. ${360}^{\circ }$

Q. A semi circle is drawn with AB as its diameter. From point C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2cm and CD= 6cm, the area of the semi-circle in sq.cm will be

1. $50\pi$
2. $81\pi$
3. Cannot be determined
4. $32\pi$

Q.

If an equilateral triangle is inscribed in a circle, then the ratio of the radius of the circle to that of the side of the triangle is -

1. 1

2. 3

3. 1/√3

4. 2

Q. In the figure, TP and TQ are tangents to the circle. $\angle PAQ={70}^{\circ }$, then the value of $\angle PTQ$ is ___

Q. A cyclic quadrilateral has one of its angles as 90 degrees. Also, its radius is 12.5 cm. The length of its diagonal is ___ cm.

Q. A circle is inscribed in a quadrilateral ABCD. Find the correct statement:

1. AB + BC = CD + AD
2. AB + CD = BC + AD
3. BD = AC
4. None of the above

Q. ABCD is a cyclic quadrilateral. The angle bisector of $\angle A,\angle B,\angle Cand\angle D$ intersect at P, Q, R and S as shown in the figure. These four points form a quadrilateral PQRS. Quadrilateral PQRS is a :

1. cyclic quadrilateral
2. rhombus
3. square
4. rectangle

Q. Answer the questions on the basis of the information given below :In the adjoining figure, I and II are circles with centers P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PO is 28 cm.



What is the ratio of the length of PQ to that of QO? (2004)

1. 1:3
2. 1:4
3. 3:8
4. 3:4

Q.

In $\Delta ABC,AB=8,AC=6,$ Altitude AD = 4.8. AE is the diameter of the circumcircle. Find the circumradius.

1. 5

2. 10

3. 15

4. Cannot be determined

Q. In the adjoining figure, 'O' is the centre of the circle and PQ , PR and ST are the three tangents. $\angle QPR={50}^{\circ }$, then the value of $\angle SOT$ is

1. can't be determined
2. ${30}^{\circ }$
3. ${75}^{\circ }$
4. ${65}^{\circ }$