MEDIUM

Earn 100

Prove that the equal chords of congruent circles subtend equal angles at their centres.

Important Questions on Triangles

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

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>Triangles>Congruence of Triangles

A wheel covers a distance of

1100 cm

in one round. The daimeter of the wheel is:

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

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:

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

The sides of a triangle are

56 cm, 90 cm

and

106 cm

The circumference of its circumcircle is:

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

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?

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

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>Triangles>Congruence of Triangles

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>Triangles>Congruence of Triangles

A B C D

is a cyclic quadrilateral such that

A B

is a diameter of the circle circumscribing it and

∠ A D C = 118 °

, then

∠ B A C

is equal to:

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

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>Triangles>Congruence of Triangles

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>Triangles>Congruence of Triangles

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:

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

Which among the following statements are certainly correct?

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

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

P B = 32 cm

and

P A = 18 cm

. The radius of the circle (in

cm

) is _____.

HARD

Mathematics>Geometry>Triangles>Congruence of Triangles

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>Triangles>Congruence of Triangles

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

∠ AOD

is ______.

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

There is a line in the plane of a circle. There are _____ maximum possibilities about the intersection of the line and the circle.

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

Two chords

A B

and

C D

of a circle intersects each other at

P

internally. If

A P = 3.5 cm

P C = 5 cm

, and

D P = 7 cm

, then what is the measure of

P B

EASY

Mathematics>Geometry>Triangles>Congruence of Triangles

A circular disc of area

0.64 π m^{2}

rolls down a length of

1.408 k m

. The number of revolutions it makes is: (Take

π = \frac{22}{7}

)

MEDIUM

Mathematics>Geometry>Triangles>Congruence of Triangles

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>Triangles>Congruence of Triangles

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

A D

. Let

O E

and

C D

intersects at

H

. Then

D H

equals

Prove that the equal chords of congruent circles subtend equal angles at their centres.

Important Questions on Triangles

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