SAT Mathematics - Circles

Exam Duration: 45 Mins Total Questions : 30

1 )

The distance between two points A and B is 3 em. A circle of radius 1.7 cm is drawn to pass through those points. Find the distance of AB from the centre of the circle

(a)
0.64
(b)
\(\sqrt { 0.64 } \)
(c)
0.8cm
(d)
0.08 cm

2 )

AB is a diameter of a circle with centre at O. DC is a chord of it such that DC II AB. If = 20^o, then is equal to

(a)
120^o
(b)
110^o
(c)
115^o
(d)
100^o

3 )

Two chords AB and CD of circle whose circle is 0, meet at the point P and = 50^o, = 40^o.Then the value of is

(a)
60^o
(b)
40^o
(c)
45^o
(d)
75^o

4 )

From four corners of a square sheet of side 4cm, four pieces, each in the shape of arc of a circle with radius 2cm are cut out. The area of the remaining portion is

(a)
(8 -\(\pi \) )sq.cm
(b)
(16- 4\(\pi \)) sq.cm
(c)
(16- 8^{\(\pi \)}) sq.cm
(d)
(4- 2^{\(\pi \)}) sq.cm

5 )

If a chord of a circle of radius 5 cm is a tangent to a circle of radius 3 ern, both circles being concentric, then the length of the chord is

(a)
10 cm
(b)
12.5 cm
(c)
8 cm
(d)
7 cm

6 )

ABC and DBC are two right triangles with common hypotenuse BC and' with their sides AC and DB intersecting at P. then product of AP.PC is equal to product of

(a)
BD.AB
(b)
PD.AP
(c)
PC.BP
(d)
BP.PD

7 )

ABC is an isosceles triangle in which AB=AC. A circle through B touching AC at its middle point D intersects AB is P, then AP=?

(a)
\(\frac { 1 }{ 4 } \quad AD\)
(b)
\(\frac { 1 }{ 4 } \quad Ac\)
(c)
\(\frac { 1 }{ 4 } \quad DC\quad \quad \)
(d)
\(\frac { 1 }{ 4 } \quad AB\)

8 )

In the given figure, the angle A of the triangle ABC is a right angle. The circle on AC as diameter cuts BC at D. If BD=9, DC=7, calculate the length of AB.

(a)
14
(b)
13
(c)
11
(d)
12

9 )

In the given figure, =42^o. Find and

(a)
128^o
(b)
138^o
(c)
118^o
(d)
none of these

10 )

Three circles have the centres at A, B, C and each circle touches the other two externally. If AB= 5cm, BC= 7cm, CA=6 cm. Find the radii of the three circles

(a)
2, 3, 4
(b)
1, 2, 3
(c)
2, 3, 5
(d)
none of these

11 )

A circle is inscribed in quadrilateral ABCD.If BC=38 cm BQ=27 cm, DC=25 cm and AD^{\(\bot \)}BC. Find the radius of the circle

(a)
7 cm
(b)
15 cm
(c)
14 cm
(d)
none of these

12 )

Two circles of radii 25 cm and 9 cm touch each other externally. Find the length of the direct common tangent?

(a)
15 cm
(b)
20 cm
(c)
25 cm
(d)
30 cm

13 )

If a straight line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively ___________ to the angles in the alternate segments.

(a)
Parallel
(b)
Perpendicular
(c)
equal
(d)
none of these

14 )

The point where a tangent line intersects a circle is called the

(a)
Centre
(b)
point of contact
(c)
end-point
(d)
none of these

15 )

A secant of a circle intersects the circle in

(a)
one point only
(b)
two points
(c)
three points
(d)
no points

16 )

How many tangents can be drawn to a circle at any project of it?

(a)
1
(b)
2
(c)
3
(d)
none of these

17 )

How many parallel tangents can a circle have at the most?

(a)
1
(b)
2
(c)
3
(d)
none of these

18 )

Two circles of radii 5 cm and 3 cm touch each other internally, the distance between their centres is

(a)
5 cm
(b)
3 cm
(c)
2 cm
(d)
8 cm

19 )

From a point Q, the length of the tangent to a circle is 24cm and the distance of Q from the centre is 25cm. The radius of the circle is

(a)
7 cm
(b)
5 cm
(c)
12 cm
(d)
1 cm

20 )

If TPand TQare the two tangents to a circle with centre O so that =100^o, then is equal to

(a)
60^o
(b)
80^o
(c)
50^o
(d)
120^o

21 )

Of any two chords of a circle, the one which is greater to nearer the

(a)
chord
(b)
circle
(c)
centre
(d)
none of these

22 )

In the given figure, a circle touches all the four sides of a quadrilateral ABCDwhose three sides are AD=6 cm, BC=7 cm, CD=4 cm. Find AD.

(a)
2 cm
(b)
5 cm
(c)
4 cm
(d)
3 cm

23 )

In the given figure, PA and PB are tangents such that PA=9cm and =60^o. Find the length of chord AB

(a)
9 cm
(b)
6 cm
(c)
7 cm
(d)
4 cm

24 )

In the following figure, 0 is the centre of the circle. The area of the sector OAPB is \(\frac { 5 }{ 18 } \) part of the area of the circIe. Find the value of x