MEDIUM
Earn 100

Determine whether the given line intersects the given circle at two distinct points, touch the circle or does not intersect the circle at any point:

L=3x+4y=10 ; C=x2+y2=9

Important Questions on Circle

MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms
In a circle with centre O, AD is diameter and AC is a chord. Point B is on AC such that OB=7 cm and ∠OBA=60°. If ∠DOC=60°, then what is the length of BC?
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
A wheel covers a distance of 1100 cm in one round. The daimeter of the wheel is:
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
The chords AB and CD of a circle interest at E. If AE=12 cm, BE=20.25 cm and CE=3DE, then the length (in cm) of CE is:
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
The sides of a triangle are 56 cm, 90 cm and 106 cm The circumference of its circumcircle is:
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
Two circles of the same radius intersect each other at P and Q. If the length of the common chord is 30 cm and the distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles?
MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms
PA and PB are two tangents from a point P outside the circle with centre O at the points A and B on it. If ∠APB=130°, then ∠OAB is equal to:
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
In a circle, chords PQ and TS are produced to meet at R. If RQ=14.4 cm, PQ=11.2 cm, and SR=12.8 cm, then the length of the chord TS is:
MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and  ∠ADC=118°, then ∠BAC is equal to:
MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms
A, B and C are three points on a circle such that the angles subtended by the chord AB and AC at the centre O are 110° and 130°, respectively. Then the value of ∠BAC is:
HARD
Mathematics>Geometry>Circle>Circles and its Related Terms
In a circle AB is a diameter and CD is a chord. AB and CD produced meet at a point P, outside the circle.If PD=15.3 cm, CD=11.9 cm and AP=30.6 cm, then the radius of the circle is :
MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC=130∘. Then ∠BAC is equal to:
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
Which among the following statements are certainly correct?
 
 
MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms
P is a point outside a circle and is away 26 cm from its centre. A secant PAB drawn from P intersects the circle at point A and B such that PB = 32 cm and PA = 18 cm. The radius of the circle (in cm) is _____.
HARD
Mathematics>Geometry>Circle>Circles and its Related Terms
Two circles of radii 15 cm and 10 cm intersect each other and the length of their common chord is 16 cm. What is the distance (in cm) between their centres?
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
AB is a chord in a circle with centre O. AB is produced to C  such that BC is equal to the radius of the circle. C is joined to O and produced to meet the circle at D. If ∠ACD = 32°, then the measure of ∠AODis ______.
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. Find the radius of the cylinder.

(use π = 227)
MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms
Two chords AB and CD of a circle intersects each other at P internally. If AP=3.5 cm, PC=5 cm, and DP=7 cm, then what is the measure of PB?
EASY
Mathematics>Geometry>Circle>Circles and its Related Terms
A circular disc of area 0.64π m2 rolls down a length of 1.408 km. The number of revolutions it makes is: (Take π=227)
MEDIUM
Mathematics>Geometry>Circle>Circles and its Related Terms

What is the circumference of the largest circle which can be inscribed in a square of side 14 cm? (π=227)

HARD
Mathematics>Geometry>Circle>Circles and its Related Terms
Consider a semicircle of radius 1 unit constructed on the diameter AB, and let O be its centre. Let C be a point on AO such that  AC : CO=2 : 1. Draw CD perpendicular to AO  with D on the semicircle. Draw OE perpendicular to AD with E on AD. Let OE and CD intersects at H. Then DH equals