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When a circle and a line are in a plane, they can have only two points of intersection.

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Important Questions on Circles

MEDIUM

Mathematics>Geometry>Circles>Interaction between Line and Circle

Define secant of a circle.

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

The perpendicular drawn from the centre of a circle to a chord bisect the chord.

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

A straight line which passes through two points on a circle is

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

In the figure, $O$ is the centre of the circle and $x^{2} + y^{2} = 25$ is the equation of the circle. Write the equation of the circle whose centre is at origin and the radius is $3$ .

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EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

Number of tangents drawn from a point inside the circle is:

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

In the figure, $O$ is the centre of the circle and $x^{2} + y^{2} = 25$ is the equation of the circle. What is the radius of the circle?

Question Image

MEDIUM

Mathematics>Geometry>Circles>Interaction between Line and Circle

Draw a circle with radius

2.5 cm

. Draw a triangle of two angles

50^{°} and 60 °

with all its sides touching a circle.

MEDIUM

Mathematics>Geometry>Circles>Interaction between Line and Circle

P A B

is a secant to a circle which intersects the circle at

A

and

B

, and

P T

is a tangent to the circle, then prove that

P A \times P B = P T^{2}

HARD

Mathematics>Geometry>Circles>Interaction between Line and Circle

Let

R

denote the circular region in the

x y -

plane bounded by the circle

x^{2} + y^{2} = 36

. The lines

x = 4

and

y = 3

divide

R

into four regions

R_{i}, i = 1, 2, 3, 4

. If

|R_{i}|

denotes the area of the region

R_{i}

and if

|R_{1}| > |R_{2}| > |R_{3}| > |R_{4}|,

determine

| R_{1} | - | R_{2} | - | R_{3} | + | R_{4} |

. (Here

|Ω|

denotes the area of the region

Ω

in the plane)

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is

12 cm

, what is the radius of each circle?

HARD

Mathematics>Geometry>Circles>Interaction between Line and Circle

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

HARD

Mathematics>Geometry>Circles>Interaction between Line and Circle

Draw a circle and two lines parallel to a given line drawn outside the circle such that one is a tangent and the other, a secant to the circle.

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

When the line

AB

intersects the circle in two distinct points

C

and

D

. Then the line

AB

is called a _____ of the circle.

MEDIUM

Mathematics>Geometry>Circles>Interaction between Line and Circle

Prove that the tangents drawn at the ends of a chords of a circle make equal angles with the chord.

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

Prove that any three points on a circle cannot be collinear.

HARD

Mathematics>Geometry>Circles>Interaction between Line and Circle

At one end

A

of a diameter

A B

of a circle of radius

5 c m

, tangent

X A Y

is drawn to the circle. The length of the chord

C D

parallel to

X Y

and at a distance

8 c m

from

A

, is

MEDIUM

Mathematics>Geometry>Circles>Interaction between Line and Circle

If a number of circles pass through the endpoints $A$ and $B$ of a line segment $A B$ , then their centres lie on the perpendicular bisector of $A B$ . Prove it.

EASY

Mathematics>Geometry>Circles>Interaction between Line and Circle

Find the unknown length