Circle
Click the appropriate answer:
1 The locus of a point that moves in a plane in such a way that its distance from a fixed point is always constant, is called
circumference circular region circular disc circle
2 A line that intersects a circle in two distinct points is called
chord secant tangent segment
3 Two circles touch each other at only one point.Which of the following is wrong ?
One circle can lie inside the other One circle is necessarily larger than the other They have only one common tangent The line passing through their centres also contains their point of contact.
4 Which of the following is true for a cyclic quadrilateral ?
It cannot be a trapezium It can be a rhombus If one side is produced, the exterior angle is equal to the adjacent interior angle. A pair of opposite angles can be 80o and 120o respectively
5 Which of these is false
A perpendicular from the centre of a circle to a chord always bisects the chord. A line joining the centres of two equal chords on the opposite sides of the centre of the circle, always passes through the centre of the circle. If two unequal circles intersect in two distinct points, the line joining these points is always bisected by the line joining the two centres. When two equal circles intersect in two distinct points, and the line joining the two centres is equal to the line joining the two intersection points, these four points are concyclic.
6 "In the following fig O is the centre, AB is a diameter and DO is to ^AB.Then which of these is false?"
ÐADO = ÐABC (AO/AC) = (AD/AB) ODCB is a cyclic quadrilateral. (AO/OB) = (OD/CB)
7 If arcs of same length but in two different circles, subtend angles of 40o and 80o resp. then the ratio of the radii of the two circles is
2 :1 1 :2 1 : 1 cannot be determined
8 A rectangle with sides 3 cm and 4 cm is inscribed in a circle.The radius of the circle is
5 cm 2.5 cm 3.5 cm 2 cm
9 "An equilateral triangle with a side = 6 cm is inscribed in a circle,.The radius of the circle is "
Ö 3 cm 2Ö2 cm 3Ö2 cm 2Ö3 cm
10 Two circular ponds of same size have been built in apark.The distance between the farthest pair of points in the two circles is 7 m.The distance between the nearest pair of points is 3 m.What is the radius of any of the circle?
1 m 2 m 3 m 1.5 m
11 A cylindrical tube fits exactly inside another.Each tube is 1 cm thick.The inner diameter of the smaller tube is 6 cm.What is the outer diameter of the outer tube?
7 cm 8 cm 9 cm 10 cm
12 A park is made up of a rectangularplot and 4 semi circular plots on each of the sides of the rectangular plot with its sides as the diameters. The area of the rectangular plot is 200 sqm and one of its sides is twice the other.What is the radius of the larger semi-circular plot.
5 m 20 m 50 m 10 m
13 Two equal circles intersect in points D & E.A straight line drawn through D intersects the circle at A and B resp.Then whichof these is true
DE ^ AB BE = EA BD = DA ÐBED = ÐDEA
14 "At 3:30 pm, the angle between the hands of a circular clock, measure "
90o 80o 75o 85o
15 "Two circles are drawn with sides AB and AC of a DABC, as their resp. diameters.The circles intersect at a point D.Then D is "
the orthocentre of DABC the incentre of DABC lies on the perpendicular bisector of line BC lies on line BC
16 AB and CD are two diameters of a circle.Which of these is false?
BC = BD CA || BD ABCD is a rectangle AD = BC
17 AB and BC are two equal chords in a circle. BP is a diameter Which of these is false ?
ÐABP = 90o Arc BCP is a semicircle AC ^ BP ÐABC is a supplement to ÐAPC
18 Chord PQ is equal to the radius of a circle.AB is a diameter not intersecting with PQ.Lines AP and BQ are produced to meet externally at R.Then ÐR =
90o 30o 60o 120o
19 "If in the following diagram, x = y, then which of the following is wrong"
O is the centre of the circle ABCD is a square AD || BC AB = DC
20 "In a cyclic quadrilateral, one of the angles is 60o and another is 90o.Then which of these is true ?"
sum of the other two angles is 180o the largest angle measures 120o One of the other two angles is the smallest the other two angles measure 120oand 60o
21 In the following fig which of the following is true ?
ÐADC = 50o AC is a diameter ÐDAC + ÐDCA = 100o AD || BC
22 "In the fig O is the centre and OA, OB, OC, OD, OE & OF are equipaced radii = r.G, H, I, J, K & Lare the midpoints of these radii.What is the perimeter of the hexagon G, H, I, J,K ,L"
6r 9r 3r r/3
23 The difference between two opposite angles in a cyclic quadrilaterals is 30o.The angles are
120oand 90o 70o and 100o 75o and 105o 65o and 95o
24 Sum of 3 angles in a cyclic quadrilateral is 320o.Sum of 2 angles of the same is 200o.Which of these cannot be one of the angles of this qaudrilateral?
60o 80o 120o 160o
25 "In a circle of radius 6 cm,AB and AC are two equal chords of 8 cm length each.Chord BC ="
16Ö2 16(Ö2/3) 16(Ö5/3) 16(Ö2/5)
26 As per the fig. Which of the following is true?
ÐACE > ÐCED ÐACE < ÐBDE ÐBED = ÐAEC ÐCEB = ÐDEA
27 4 coins each of diameter 2 cm are placed so that each coin touches 2 other coins.What is the maximum area of the figure formed by joining their centres?
4 sqcm 2 sqcm 1 sqcm insufficient information
28 "How many circles of radii 1 cm each, can fit into a square of area 64 sqcm?the circles can touch each other in 1 point, but cannot intersect each other, or be contained inside another."
64 8 16 32
29 "Three circles that touch each other only at on point externally, have radii in the ratio 3:2:1.the Perimeter of the triangle formed by joining their centres is 24 cm.What are the 3 radii?
6,4,2 9,6,3 12,8,4 3,2,1
30 In this diagram what is the measure of ÐABC ? (O is the centre of the circle)
70o 60o 50o 120o
31 In the following diagram O is the centre of one circle. The measure of x is
80o 160o 100o 40o
32 "Two circles of radii 7 and 4 cm resp, touch each other at one point only.Which of these is correct?"
The distance between their centres cannot be 3 cm The distance between their centres cannot be 11cm " A line passingthrough the point of intersection, necessarily intersects each circle in 2 points." The maximum length of a line segment that passes through the point of intersection and whose extremities lie on each circle is 22cm.
33 Two circles in a plane touch each other in at least one point. Their radii are 3 and 5 cm resp.The distance between their centres cannot be
6 cm 4 cm 1 cm 8 cm
34 Two parallel chords in a circle are resp. 6 and 2 cm away from the centre.The length of the smaller chord is 16 cm.Which of the following is false?
the distance between the chords can be 4 cm The distance between their chords can be 8cm the radius of the circle is 8 cm The larger chord is 19.6 cm
35 The area of a square inscribed in a circle of radius 4 cm is
16 sqcm 24 sqcm 32 sqcm 64 sqcm
36 A chord divides a circular region into two parts that are called
segments arcs sectors circular disks
37 A tangent passes through 2 points on a circle.These two points are
concurrent coincident congruent concyclic
38 The angle subtended by a minor arc at the centre of the circle cannot be
90o obtuse acute straight angle
39 The condition for a trapezium to be cyclic is
Its parallel sides must be equal Its non-parallel sides must be equal Atleast one of its angles must be 90o Any two adjacent angles must total up to 180o
40 The opposite angles of a cyclic quadrilateral are
supplementary complementary equal always unequal
41 The angle subtended at the centre of a circle by any of the sides of a regular polygon is
45o 60o 90o insufficient information
42 Which of these is false about two unequal circles
They can intersect in one point They can intersect in three points They need not intersect at all One can lie inside the other without touching the other.
43 Which of these is false for a triangle inscribed in a circle
The angle bisectors always meet within the circle The perpendicular from vertices to opposite sides can meet outside the circle The medians meet at the centre of the circle A right angled triangle lies entirely within a semicircle
44 ABCDEF is a regular hexagon inscribed in a circle.Which of the following is false?
ÐBCE = 90o ÐAFB = 30o ÐBCE + ÐCEF = 180o ÐCDE + ÐFAB = 180o
45 "In a circle with centre O,chord AB is half the length of the diameter.How far is it from the centre of the circle? (r = length of the radius)"
r2 - ( r)2/4 r/2Ö3 rÖ3 r(Ö3)/4
46 Two equal circles touch each other externally at only one point.A third circle is drawn through their centres.Then
The third circle is equal to both The third circle is smaller than both The third circle is always larger than both The third circle can never be smaller than the two
47 A regular hexagon is inscribed in a circle of radius r.What is its area?
(Ö3)/2r2 3(Ö3)r2 (Ö3)/4 r2 3(Ö3)/2 r2
48 Which of these circles are not equal
One has a diameter of 7 cm and the other has a radius of 3.5 cm They intersect each other in 3 points They intersect in two points and the line joining these points is bisected by the line joining their radii The areas of equilateral triangles inscribed in them are equal
49 "In the fig ,what is Ðx ?"
110o 120o 140o 160o
50 "In the fig,what is Ð x ? O is the centre of thecircle"
100o 110o 160o 150o