Length of Chord

Q.

A chord 12 cm long is 8 cm away from the centre of the circle. What is the length of a chord which is 6 cm away from the centre?

1. 16 cm

2. 12 cm

3. 14 cm

4. 18 cm

Q.

Two parallel chords 10 centimeters and 24 centimeters long are drawn on the same side of the centre of a circle of radius 13 centimeters. Find the distance between the chords.

1. 5 cm

2. 6.5 cm

3. 7 cm

4. 8.5 cm

Q.

In a circle, two parallel chords of lengths 8 cm and 12 cm are 10 cm apart. Then the distance of the shorter chord from the centre is

1. 4 cm

2. 5 cm

3. 8 cm

4. 6 cm

Q.

A chord 6 cm long is 1 cm away from the centre of the circle. What is the length of a chord which is 2 cm away from the centre?

Q.

In a circle, two parallel chords of lengths 16 cm and 24 cm are 20 cm apart. Then the radius of the circle is

1. $\sqrt{224}$ cm

2. 15 cm

3. $\sqrt{108}$ cm

4. $\sqrt{208}$ cm

Q.

A chord 8 cm long is 3 cm away from the centre of the circle. What is the length of a chord which is 4 cm away from the centre?

1. 2 cm

2. 6 cm

3. 8 cm

4. 10 cm

Q.

In the semicircle shown, the top chord is parallel to the diameter. What is its length?

1. 5 cm

2. 10 cm

3. 16 cm

4. 20 cm

Q.

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle.

___

Q.

A chord 16 cm long is 6 cm away from the centre of the circle. Then the chord of length 8 cm is ___ cm away from the centre.

1. $3\sqrt{21}$ cm

2. $\sqrt{21}$ cm

3. $2\sqrt{21}$ cm

4. $4\sqrt{21}$ cm

Q.

In a circle, two parallel chords of lengths 6 cm and 8 cm are 6 cm apart. Then the distance of chord of length 6 cm from the centre is

1. $\frac{43}{12}$ cm

2. 4 cm

3. $\frac{52}{12}$ cm

4. 6 cm

Q. Two parallel chords, 10 cm apart, of lengths 8 cm and 12 cm, respectively are there in a circle. Find the distance of the shorter chord from the centre.

Q.

In the fig., it is given that:
$XY=6cm$
$\angle XOY=\angle MON={85}^{\circ }$.
The length of the chord MN is ___cm.

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

Q.

In a circle, two parallel chords of lengths 4 cm and 10 cm are 5 cm apart. Then the distance of the longer chord from the centre is ________.

1. 0.1 cm

2. 0.2 cm

3. 0.3 cm

4. 0.4 cm

Q. In a circle of radius 5 cm PQ and RS are two prajallel chords of length 8 cm & 6 cm respectively lying onthe opposite sides of sides of center The distance between the chords is

1. 1 cm
2. 5 cm
3. 6 cm
4. 7 cm

Q. AB and CD are two parallel chords of a circle with centre O such that AB = 6 cm and CD = 12 cm. The chords are on the same side of the centre and the distance between them is 3 cm. Construct line segment OL such that it bisects chords AB and CD perpendicularly at point L and M respectively.
Find the radius of the circle.

Q. A gentleman invites a party of $m+n(m\ne n)$ friends to a dinner and places $m$ at one table $T_1$ and $n$ at another table $T_2$, the table being around. If not all people shall have the same neighbour in any two arrangement, then the number of ways in which he can arrange the guest, is

1. $\frac{(m+n)!}{4mn}$
2. $\frac{1}{2}\frac{(m+n)!}{mn}$
3. $2\frac{(m+n)!}{mn}$
4. $None$

Q.

If I draw two circles of radius 3 cm and 5 cm with common centre and draw a line AB such that it is chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.

1. 2, 2.35

2. 2.16, 2.35

3. 3, 2

4. 2.35, 2

Q. AB and CD are two parallel chords of a circle with centre O such that AB = 6 cm and CD = 12 cm. The chords are on the same side of the centre and the distance between them is 3 cm. Construct line segment OL such that it bisects chords AB and CD perpendicularly at point L and M respectively.
Find the radius of the circle.

Q. Two parallel chords of equal length 18 cm are drawn inside a circle of radius 15 cm Find the distance between the chords

1. 24 cm
2. 18 cm
3. 30 cm
4. 12 cm

Q. A chord 8 cm long is 3 cm away from the centre of the circle A. Calculate the length of a chord that is 4 cm away from the centre of circle A.

Q. A chord 8 cm long is 3 cm away from the centre of the circle A. Calculate the length of a chord that is 4 cm away from the centre of circle A.

Q. Let $ABCD$ be a quadrilateral inscribed in a circle. Suppose $AB=\sqrt{2+\sqrt{2}}$ and $AB$ subtends ${135}^{\circ }$ at the centre of the circle. Find the maximum possible area of $ABCD$.

Q. In the adjoining figure, AB and CD are two parallel chords and O is the centre. If the radius of the circle is 15 cm, find the distance MN between the two chords of length 24 cm and 18 cm respectively.

Q. A field is in the shape of a trapezium whose parallel sides are $25m$ and $10m$. The non-parallel sides are $14m$ and $13m$. Find the area of the field.

Q. Draw a rhombus, having each side of length $3.5cm$ and one of the angles as ${40}^{\circ }$.

Q. In the given figure, $O$ is the center of the circle and is $ABC$ subtends an angle ${130}^o$ at the center. If $AB$ extended to $P$, find $\angle PBC$.