

SAT Mathematics - Circles
Exam Duration: 45 Mins Total Questions : 30
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
AB is a diameter of a circle with centre at O. DC is a chord of it such that DC II AB. If = 20o,
then is equal to
- (a)
120o
- (b)
110o
- (c)
115o
- (d)
100o
Two chords AB and CD of circle whose circle is 0, meet at the point P and = 50o,
= 40o.Then the value of
is
- (a)
60o
- (b)
40o
- (c)
45o
- (d)
75o
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
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
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
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)
\(\frac { 1 }{ 4 } \quad AB\)
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
In the given figure, =42o. Find
and
- (a)
128o
- (b)
138o
- (c)
118o
- (d)
none of these
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
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
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
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
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
A secant of a circle intersects the circle in
- (a)
one point only
- (b)
two points
- (c)
three points
- (d)
no points
How many tangents can be drawn to a circle at any project of it?
- (a)
1
- (b)
2
- (c)
3
- (d)
none of these
How many parallel tangents can a circle have at the most?
- (a)
1
- (b)
2
- (c)
3
- (d)
none of these
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
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
If TPand TQare the two tangents to a circle with centre O so that =100o, then
is equal to
- (a)
60o
- (b)
80o
- (c)
50o
- (d)
120o
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
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
In the given figure, PA and PB are tangents such that PA=9cm and =60o. Find the length of chord AB
- (a)
9 cm
- (b)
6 cm
- (c)
7 cm
- (d)
4 cm
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
- (a)
100o
- (b)
75o
- (c)
150o
- (d)
none of these
In the adjoining figure, find the perimeter of the figure where AED is a semicircle and ABCD is a rectangle
- (a)
152 cm
- (b)
38 cm
- (c)
76 cm
- (d)
104 cm
A square is circumscribing a circle. The side of the square is 14cm. Find the area of the square not included in the circle
- (a)
21 cm2
- (b)
42 cm2
- (c)
48 cm2
- (d)
196 cm2
If the diameter of a semicircle protractor is 14 cm, then, find the perimeter
- (a)
36 cm
- (b)
18 cm
- (c)
27 cm
- (d)
30 cm
A bicycle wheel makes 5000 revolution in moving llkIn. Find the circumference of the wheel.
- (a)
55 cm
- (b)
110 cm
- (c)
165 cm
- (d)
220 cm
A chord of a circle of radius 6 em subtends an angle of measure 60° at the centre. Find the area of the minor segment formed by this chord
- (a)
\(3\left( 2\pi -3\sqrt { 3 } \right) cm^{ 2 }\\ \)
- (b)
\(3\left( 3\pi -\sqrt { 3 } \right) cm^{ 2 }\\ \)
- (c)
\(3\left( 3\pi -2\sqrt { 3 } \right) cm^{ 2 }\\ \)
- (d)
\(3\left( 3\pi -3\sqrt { 3 } \right) cm^{ 2 }\\ \)
In the given figure, find the length of the chord AB if PA=6cm and = 60o
- (a)
2 cm
- (b)
4 cm
- (c)
6 cm
- (d)
5 cm