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Standard IX

Mathematics

Perpendicular from the Centre of a Circle to a Chord

Let OM and ON...

Question

Let OM and ON be perpendiculars drawn from the centre O of a circle to chords AB and CD respectively. If AB= 10 cm, then CD= .

10 cm

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5 cm

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2.5 cm

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7.5 cm

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Solution

The correct option is A 10 cm

From figure, it is clear that $O M ⊥ A B, O N ⊥ C D$ and OM=ON.
We know the property that the chords equidistant from the centre of a circle are equal in length.
$⟹ A B = C D$
Thus, $C D = 10 cm .$

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Similar questions

Q. In the given figure,

O

is the centre of the circle.

A B

and

C D

are two chords of the circle.

O M

is perpendicular to

A B

and

O N

is perpendicular to

C D

A B = 24 c m, O M = 5 c m, O N = 12 c m

. Find the:
(i) radius of the circle.
(ii) length of chord

C D

Q. In the figure given,

O

is the centre of the circle.

A B

and

C D

are two chords of the circle.

O M

is perpendicular to

C D

and

O N

is perpendicular to

A B

A B = 24 c m, O N = 5 c m, O M = 12 c m

. Find the length of chord

C D

Q. In the given figure, O is the centre of a circle. AB and CD are its two chords. If OM

⊥

AB and ON

⊥

CD and OM = ON, then

O

is the centre of the circle.

A B

and

C D

are two chords of the circle.

O M ⊥ A B

and

O N ⊥ C D

. If

O M = O N = 3

cm and

A M = B M = 4.5

cm, then

C D

is equal to

In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB||CD and AB = 10 cm then CD = ?

(a) 5 cm

(b) 12.5 cm

(d) 10 cm

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Let OM and ON be perpendiculars drawn from the centre O of a circle to chords AB and CD respectively. If AB= 10 cm, then CD= .

The correct option is A 10 cm From figure, it is clear that OM⊥AB,ON⊥CD and OM=ON. We know the property that the chords equidistant from the centre of a circle are equal in length. ⟹AB=CD Thus, CD=10 cm.

The correct option is A 10 cm

From figure, it is clear that $O M ⊥ A B, O N ⊥ C D$ and OM=ON.
We know the property that the chords equidistant from the centre of a circle are equal in length.
$⟹ A B = C D$
Thus, $C D = 10 cm .$