Chord Theorem 2

Q. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m 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 6 m each, what is the distance between Reshma and Mandip?

Q.

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = ____ OD.

___

Q. 8.Chord AB of the circle x²+y², =100 passes through the point (7, 1) and substends an angle of 60 at the circumference of the circle.If m1 and m2 are the slopes of 2 such chords then the value of m1.m2 is

Q. In the given figure, AB and CD are two equal chords of the circle with centre O. OP and OQ are perpendiculars of the chord AB and CD respectively. If $\angle POQ={80}^{\circ },$ then what is the value of $\angle APQ$?

1. ${50}^{\circ }$
2. ${40}^{\circ }$
3. ${30}^{\circ }$
4. ${60}^{\circ }$

Q. Question 8
The area of the square that can be inscribed in a circle of radius 8 cm is
(A) $256c{m}^2$
(B) $128c{m}^2$
(C) $64\sqrt{2}c{m}^2$
(D) $64c{m}^2$

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.

1. 6 cm

2. 8 cm

3. 10 cm

4. 11 cm

Q.

Distance between equal chords, $AB$ and $CD$ of a circle with centre, $O$ and radius, $5cm$ is $8cm$. Find the length of the the chords.

1. $8cm$

2. $6cm$

3. $10cm$

4. $12cm$

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.

In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP $>$ PB. Then, AP is–

1. 24 cm

2. 8 cm

3. 6 cm

4. 12 cm

Q.

$PQ\text{and}RQ$ are chords of a circle equidistant from the centre. Prove that the diameter passing through $Q$ bisects $\angle PQR\text{and}\angle PSR$.

Q.

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

1. 2 cm

2. 1 cm

3. 3 cm

4. 4 cm

Q.

In the following figure, if the chords AB and CD are equal to 6 cm then the distance of the chords from the centre of the circle of radius 5 cm will be:

1. 4 cm, 4 cm

2. 4 cm, 8 cm

3. 8 cm, 4 cm

4. 8 cm, 8 cm

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.

The figure is a circle with centre O and diameter 10 cm. PQ = 1 cm. Then the length of RS is

1. 3 cm

2. 6 cm

3. 4 cm

4. 8 cm

Q. The angles subtended by arc XY and MN on the centre of the circle are 45° each. The length of the chord XY = 18 cm, then find the length of the chord MN.

Q.

Draw a circle on a tracing paper and draw two equal chords and drop a perpendicular from center to the chord. Fold the paper such that the two chords coincide. You will find that the two perpendiculars also coincide.

1. True

2. False

Q.

Let AB and CD be two equal chords of a circle which intersect within the circle centered at O, as shown below.

Then which of the following is/are true?

1. AP + DP = CP + BP

2. BP = DP, but AP $\ne$ CP

3. AP = CP and BP = DP

4. AP = CP, but BP $\ne$ DP

Q.

In the figure, $P$ and $Q$ are the points of intersection of two circles with centres $O$ and $O^{\prime }.$ If straight lines, $APB$ and $CQD$ are parallel to $O{O}^{\prime },$ then what is the ratio of $O{O}^{\prime }$ and $AB?$

1. $1:3$

2. $1:2$

3. $1:4$

4. $3:4$

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.

In the adjoining figure, OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter, then which of the following are true?

1. $AC=2OD$

2. $\frac{AC}{DO}=\frac{BC}{BO}$

3. $\frac{AC}{BO}=\frac{BC}{DO}$

4. $OD\parallel AC$

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.

AB & CD are two equal chords of a circle with centre O which intersect each other at the right angle at point P. If the perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a _______.

1. square

2. kite

3. rhombus

4. rectangle

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.

In the given figure, a circle with centre O has diameter 16 cm. If PQ = 2 cm, then the measure of RS is

1. $2\sqrt{7}cm$

2. $2\sqrt{28}cm$

3. $\sqrt{28}cm$

4. $4\sqrt{7}cm$

Q. A chord of length 30 cm is drawn at a distance of 8 cm from the centre of a circle. Find out the radius of the circle.

Q.

S1: AM = $\frac{AP}{2}$, BN= $\frac{BP}{2}$

S2: OO' = AM + BN

Which of the above statements are true?

1. Only S1 is true.

2. Only S2 is true.

3. S1 is true & S2 is false.

4. Both statements are true.

Q.

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

1. AYBA, AXBA

2. XAYX, XBYX

3. AXBA, AYBA

4. XBYX, XAYX

Q.

An equilateral triangle ABC is inscribed in a circle with centre $O.$ Then, $\angle BOC$ is equal to:

1. 30°

2. 60°

3. 90°

4. 120°

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 = 8 cm and OD = 3 cm, then find the circumradius.

1. 4 cm

2. 5 cm

3. 8 cm

4. 10 cm