Perpendicular from the Centre of a Circle to a Chord

Q.

Find the diameter of a circle whose radius is $4cm$

Q. 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= .

1. 10 cm
2. 5 cm
3. 2.5 cm
4. 7.5 cm

Q. O is the centre of the circle whose radius is 17 cm. Find the distance of the chord from the centre if the length of the chord is 30 cm.

1. 11 cm
2. 8 cm
3. 7 cm
4. 14 cm

Q. In the below figure, BC= ___.

1. 4 cm
2. 3 cm
3. 6 cm
4. 8 cm

Q. Question 1
Write True or False and justify your answer :

Two chords AB and CD of a circle are each at a distance of 4 cm from the centre, then AB = CD.

Q.

A circle has radius $\sqrt{2}cm$. It is divided into two segments by a chord of length $2cm$. Then the angle subtended by the chord at a point in major segment is:

1. $75°$

2. $60°$

3. $80°$

4. $45°$

Q. A circle has a radius of 5 cm and a chord AB of 8 cm. How far is the midpoint of the chord from the centre of the circle?

1. 3 cm
2. 4 cm
3. 5 cm
4. 2.5 cm

Q. In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ___.

1. 1 cm
2. 3 cm
3. 2 cm
4. 5 cm

Q. 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= .

1. 10 cm
2. 5 cm
3. 2.5 cm
4. 7.5 cm

Q. The perpendicular drawn from the centre of the circle to a chord divides the chord in the ratio .

1. 2:1
2. 1:2
3. 1:1

Q. The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD =16 cm and EB = 4 cm, then find the radius of the circle.

Q. The radius OB of a circle is perpendicular to a chord PQ of length 12 cm. If the radius meets the chord at a point A, then the length of AP =.

1. 4 cm
2. 5 cm
3. 6 cm

Q.

The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC.

1. 5.6 cm

2. 9.6 cm

3. 10.6 cm

4. 11.6 cm

Q.

Find the length of a chord which is at a distance of 3 cm from the centre of a circle of radius 5 cm.

[2 Marks]

Q.

What is the relation between AM & MB in the given figure?

1. AM = MB

2. AM = 2MB

3. 2AM = MB

4. 3AM = 2MB

Q.

The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E . If CD =16 cm and EB = 4 cm, then find the radius of the circle.

1. 10 cm

2. 11 cm

3. 8 cm

4. 6 cm

Q. In the given figure, AB is a chord that is 3 cm away from the centre O of a circle of radius 5 cm. If OE is the angle bisector of $\angle AOB$ and if it bisects AB at ${90}^{\circ },$ then what is the length of AB?

1. 6 cm
2. 3 cm
3. 8 cm
4. 5 cm