Chord Theorem 2

Q.

Two circles of radii $5cm$ and $6cm$ with common centre are drawn. There is a line $AB$ such that it is chord to both the circles. $CD=8cm.$ Find the distance of the chord from centre and the length of $AC$ respectively.

1. $3cm,1.19cm$

2. $2.55cm,2.35cm$

3. $3cm,2cm$

4. $2.16cm,2.35cm$

Q.

Two circles whose centres are $O$ and $O^{\prime }$ intersect at $P$. Through $P$, a line parallel to $O{O}^{\prime }$, intersecting the circle at C and D is drawn as shown. Then $CD=2O{O}^{\prime }$.

1. True

2. False

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.

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the distance between AB and CD.

1. 8 cm

2. 7 cm

3. 11 cm

4. 10 cm

Q.

Two circles of radii $4cm$ and $3cm$ intersect at two points and the distance between their centres is $5cm$. Find the length of the common chord.

1. $7cm$

2. $4.8cm$

3. $5.5cm$

4. $2.8cm$

Q.

In the given figure, lengths of the chords $AB$ and $CD$ are $12cm$ and $18cm$ respectively and distance between them is $15cm$. Find the radius of the circle.

1. $\sqrt{119}cm$

2. $\sqrt{113}cm$

3. $\sqrt{117}cm$

4. $\sqrt{114}cm$

Q.

In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 24 cm and OD = 5 cm, then find the circumradius.

1. 10 cm

2. 11 cm

3. 12 cm

4. 13 cm

Q.

The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm & 34 cm, the distance between their centers is ____ cm.

1. 30

2. 28

3. 24

4. 32

Q.

Four points A, B, C, D are given on a circle. Line segment AB and CD are parallel. Find the area of the figure formed by joining these points (in ${cm}^2$).

1. 98

2. 49

3. 7

4. 28

Q.

The perpendicular to a chord, from the centre of the circle divides the chord in ratio ___.

1. 1 : 2

2. 1 : 1

3. 1 : 3

4. 1 : 4