Chord Theorem 1

Q.

O is the centre of the circle of radius 5 cm, OP is perpendicular to AB, OQ is perpendicular to CD, AB || CD, AB = 6 cm and CD = 8 cm. Determine PQ.

1. 1cm

2. 2cm

3. 3cm

4. 4cm

Q.

In the figure, the diameter $CD$ of a circle with centre $O$ is perpendicular to the chord $AB$. If $AB=12cm$ and $CE=3cm$, find the radius of the circle (in $cm$)

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.

Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

1. $\sqrt{a^2-b^2}$

2. $\sqrt{a^2+b^2}$

3. $2\sqrt{a^2-b^2}$

4. $2\sqrt{a^2+b^2}$

Q.

In a circle of radius 5 cm, AB and AC are two chords of 6 cm each. Then the length of the chord BC is

1. $9.6$ cm

2. $8.4$ cm

3. $8.8$ cm

4. $9.2$ cm

Q.

The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Then the distance of the chord from the centre is

1. 6 cm
2. 12 cm

3. True

4. False

Q.

In a circle, two parallel chords of lengths 4 cm and 6 cm are 5 cm apart. Then the radius of the circle is

1. $\sqrt{13}$ cm

2. $2\sqrt{13}$ cm

3. $\frac{1}{\sqrt{13}}$ cm

4. $\frac{\sqrt{13}}{2}$ cm

Q. In the following figure OM=ON and AB=12cm. Then CN= .

1. 6cm
2. 8cm
3. 10cm
4. 9cm

Q.
The figure shows a circle with centre O, in which $OE\perp CD$. If CD = 8 cm and EB = 2 cm, then find the radius of the circle.

1. 2 cm
2. 5 cm
3. 10 cm
4. 8 cm

Q.

In any triangle $ABC$, if the angle bisector of $\angle A$ and perpendicular bisector of $BC$ intersect, prove that they intersect on the circumcircle of the $△ABC$.

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, $AC$.

1. $4cm$

2. $5cm$

3. $7cm$

4. $8cm$

Q.

In the circle shown alongside, the chords AB and AC are of same length. The bisector of $\angle$A intersects the chord BC at D and meets the circle at E. Then which of the following is/are true?

1. D is the midpoint of BC.

2. D divides BC in the ratio 1:2.

3. AE is perpendicular bisector of chord BC

4. AE is a diameter

Q.

CD is the diameter of the circle centered at O, which meets the chord AB at E. OE$\perp$AB and AB = 8 cm. If DE = 3cm , then the radius of the circle is

1. $4\frac{1}{6}cm$
2. $3\frac{1}{6}cm$
3. $4\frac{1}{3}cm$
4. $4\frac{1}{5}cm$

Q. The given figure shows two chords drawn on either side of the diameter, making equal angles with the diameter. Calculate the length of the other chord if the length of one chord is 18 units. [2 marks]

Q. In the given figure, $O$ is the centre of the circle with radius $20\text{cm}$ and $OD$ is perpendicular to $AB$. If $AB=32\text{cm}$, find the length of $CD$.

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 = 16 cm and OD = 6 cm, then find the circumradius.

1. 5 cm

2. 8 cm

3. 15 cm

4. 10 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.

Q.

In the diagram, select the major arc and the minor arc of the circle, with respect to the chord AB.

1. XAY, XBY

2. AXB, AYB

3. XBY, XAY

4. AYB, AXB

Q. Two equal and parallel chords, $AB$ and $CD$ are at a distance of 10 cm from each other. Find the distance of chord $AB$ from the centre.

1. $20cm$
2. $6cm$
3. $12cm$
4. $5cm$

Q. Perpendicular from the centre of the circle to the chord bisects the chord in what ratio?

1. 1:1
2. 2:1
3. 1:2
4. 1:4

Q. In the given figure, OC is perpendicular to the chord AB. If AB = 8 cm, then the value of BC is .

1. 6 cm
2. 8 cm
3. 4 cm
4. 3 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. 10 cm

2. 7 cm

3. 8 cm

4. 11 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. Consider the below figure where the diameter AB bisects the chord PQ at the point R. If BR = 4 cm, then what is the radius of the circle?

1. 10

Q. If $AB$ is a chord and $P$ is a point on $AB$ such that $AP=8$ cm, $PB=5$ cm and $P$ is $3$ cm from the centre of the circle, find the radius.

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?

Q. The line drawn through the centre to bisect a chord is not perpendicular to the chord.

1. False
2. True

Q. The radius of a circle is $16cm$. The mid point of a chord of the circle lies on the diameter perpendicular to the chord and its distance from the near end of the diameter is $3cm$; If the length of that chord is $m\sqrt{87}$ cm, then the value of $m$ is

1. $4$
2. $2$
3. $8$
4. $1$

Q.

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

1. $10cm$

2. $12cm$

3. $13cm$

4. $11cm$

Q.

A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.

1. 4 cm

2. 5 cm

3. 8 cm

4. 9 cm