The perimeter of a semicircular protractor is 324 cm Calculate the radius of the protractor in cm

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

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:

EASY

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

Which among the following statements are certainly correct?

EASY

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

Two circles of the same radius intersect each other at

P

and

Q

. If the length of the common chord is

30 c m

and the distance between the centres of the two circles is

40 c m

, then what is the radius (in

c m

) of the circles?

EASY

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

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 - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

In the figure, $O$ is the centre of the large circle. The centre of the small circle is $C$ . $O P$ is a tangent to the small circle. $∠ BOQ = 50 °$ .

$∠ APO =$ _____ $°$

EASY

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

A wheel covers a distance of

1100 cm

in one round. The daimeter of the wheel is:

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

What is the circumference of the largest circle which can be inscribed in a square of side $14 c m$ ? ( $π = \frac{22}{7}$ )

HARD

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

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?

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

In the figure, $O$ is the centre of the large circle. Centre of the small circle is $C$ . $O P$ is a tangent to the small circle. $∠ BOQ = 50 °$ .

$∠ POQ =$ _____ $°$

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

In the figure, $O$ is the centre of the large circle. Centre of the small circle is $C$ . $O P$ is a tangent to the small circle. $∠ BOQ = 50 °$ .

$∠ OAQ =$ _____ $°$

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

The wall around a semicircular garden is

180 m

long. The area of the garden is (Take

π = \frac{22}{7}

)

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

In the given figure, $A B C D E$ is a pentagon inscribed in a circle such that $A C$ is a diameter and side $B C ∥ A E$ . If $∠ B A C = 50 °$ , find giving reason $∠ A C B$ .

EASY

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

The chords

AB

and

CD

of a circle interest at

E

. If

AE = 12 cm

,

BE = 20.25 cm

and

CE = 3 DE

, then the length (in cm) of

CE

is:

HARD

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

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 - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

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

?

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

ABCD

is a cyclic quadrilateral such that

AB

is a diameter of the circle circumscribing it and

∠ ADC = 130^{\circ}

. Then

∠ BAC

is equal to:

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

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:

HARD

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

Consider a semicircle of radius

1

unit constructed on the diameter

A B

, and let

O

be its centre. Let

C

be a point on

A O

such that

A C : C O = 2 : 1

. Draw

C D

perpendicular to

A O

with

D

on the semicircle. Draw

O E

perpendicular to

A D

with

E

on

A D

. Let

O E

and

C D

intersects at

H

. Then

D H

equals

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

In the figure, $O$ is the centre of the large circle. Centre of the small circle is $C$ . $O P$ is a tangent to the small circle. $∠ BOQ = 50 °$ .

$∠ OCP =$ _____ $°$

MEDIUM

Mathematics>Geometry - II>Circle>Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle

If the perimeter of a semicircle is

36 cm

, then its radius is

The perimeter of a semi-circular protractor is 32.4 cm. Calculate the radius of the protractor in cm

Important Questions on Circle

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