Perpendicular from Center to a Chord

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

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

Q.

Represent $\sqrt{9.3}$ on the number line.

Q.

An equilateral triangle ABC is inscribed in a circle of radius 12 cm, which is centered at O, as shown below. Calculate the length of the sides of this triangle.

Q. Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 10 cm. [use $\sqrt{75}=8.66$]

1. 17 cm
2. 17.32 cm
3. 18.46 cm
4. 19 cm

Q. In a circle with center O, a perpendicular is dropped from the center to a chord PQ. Find the length of PO, if length of PQ = 24 cm and KO = 5 cm.

1. 8 cm
2. 9 cm
3. 13 cm
4. 14 cm

Q.

A cylinder with a radius of $4inches$ and a height of $6inches$ is similar to a cylinder with a radius of r inches and a height of $9inches$. What is the value of $r$?

Q.

Question 3
The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Q. Find the length of a chord that is at a distance of 4 cm from the centre of a circle of radius 6 cm.

Q. The radius of a circle is 8 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.

Q. In the given circle with centre O, if the radius of the circle is 13 cm, OQ⊥PR and OQ = 5 cm. Find PR.

1. 12 cm
2. 13 cm
3. 24 cm
4. 5 cm

Q.

The length of the chord passing through the centre of a circle represents the radius of a circle.

1. True
2. False

Q. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius $5m$ drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is $6m$ each, what is the distance between Reshma and Mandip?

Q.

The line joining the centre of a circle to the mid-point of a chord is always:

1. parallel to the chord

2. perpendicular to chord

3. equal to the chord

4. tangent to the chord

Q.

In the given figure, radius of the circle is \(5~cm\) and perpendicular distance from the centre of the circle to the chord \(AC\) is \(3~cm\).
Find the length of the chord \(AC\).

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 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.

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

1. 2AM = MB

2. AM = MB

3. AM = 2MB

4. 3AM = 2MB

Q. Question 2
In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to

(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) 5 cm

Q.

In the given figure, radius of the circle is $5cm$ and perpendicular distance from the centre of the circle to the chord $AC$ is $3cm$.
Find the length of the chord $AC$.

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. 6 cm

2. 8 cm

3. 10 cm

4. 11 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. The line drawn through the centre of a circle to bisect a chord is _________ the chord.

1. equal to
2. perpendicular to
3. parallel to
4. double

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.

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. 6 cm

2. 10 cm

3. 8 cm

4. 11 cm