Chord

Q.

(a) Is every diameter of a circle also a chord?

(b) Is every chord of a circle also a diameter?

Q. Question 14
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.

Q.

Radius of a circle is also a chord of the circle.

1. True

2. False

Q.

A circle has finite number of equal chords.

1. True

2. False

Q.

In the given circle, identify the center, radii, diameter and chords.

1. Center-O; Radii - OA, OC, OB ;
   Diameter AB ; Chords - BC , AB

2. Center-O; Radii-AC ;
   iameter AB ; Chords- OA, OB, OC ;

3. Center - O; Radii - OA, OC ;
   Diameter - AB ; Chords - BC

4. Center - O, Radii -OA ;
   Diameter AB ; Chords-BC

Q.

If AB is a chord of a circle, P and Q are the two points on the circle different from A and B, then

1. $\angle APB=\angle AQB={180}^{o}or\angle APB=\angle AQB$

2. $\angle APB+\angle AQB={180}^o$

3. $\angle APB+\angle AQB={90}^o$

4. $\angle APB=\angle AQB$

Q.

The lines joining the origin to the points of intersection of the line $y=mx+c$and the circle $x^2+y^2=a^2$ will be mutually perpendicular, if

1. $a^2(m^2+1)=c^2$

2. $a^2(m^2–1)=c^2$

3. $a^2(m^2+1)=2c^2$

4. $a^2(m^2–1)=2c^2$

Q.

Prove that line is a circle of infinite radius.

Q. P is the centre of the circle. Chord AB and chord CD intersect on the diameter at the point Q. If $\angle$AQP $\cong$ $\angle$PQD, then AB = CD.

1. True
2. False

Q. In Fig. 4, find the measure of arc ADC, if ∠OAB = 30° and ∠OCB = 50°.

Q. Question 2 (ii)
Write True or False. Give reasons for your answers.

(ii) A circle has only finite number of equal chords.

Q.

A chord is a line segment that joins any two points on the circumference of the circle.

1. False

2. True

Q. O is the centre of the circle. If $\angle$BOA = 90° and $\angle$COA = 110°, find $\angle$BAC.

Q. 6.OA and OB are respectively perpendiculars to chords CD and EF of the circle whose centre is O. If OA=OB then prove arc CE congruent to arc DF.

Q.

Which of the following is a chord?

1. Segment
2. Arc
3. Diameter
4. Radius

Q. 16. If a point T is 6 units from the centre of a circle of radius 10 units, then the total number of different chords of the circle passing through T and have integral length is (A) 8 (B) 4 (C) 5 (D) 10

Q.

The latus rectum of the parabola$y^2=4ax$, whose focal chord is $PSQ$, such that $SP=3$ and $SQ=2$ are given by

1. $\frac{24}{5}$

2. $\frac{12}{5}$

3. $\frac{6}{5}$

4. $\frac{1}{5}$

Q. A circle has radius 15 cm. Find the length of its longest chord?

Q.

If $BC$ is a diameter of a circle with centre $O$ and $OD$ is perpendicular to the chord $AB$ of a circle, show that $CA=2OD$.

Q. locus of centres of the circles which touch the two circles x2+y2=16 and x2+y2=16x externally i

Q. In a circle of diameter 10 cm, length of each of the two equal and parallel chords is 8 cm. What is the distance between the chords?

Q. 34. The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length of AD.

Q.

TRUE or FALSE & explain how :

1) If a circle is divided into 3 equal arcs, then each is a major arc.

2) Sector is the region between the chord and it's corresponding arc.

3) The degree measure of an arc is the compliment of the central angle containing the arc.

Q.

The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length is–

1. √5 cm

2. 2√5 cm

3. 2√7 cm

4. √7 cm

Q. The radius of a circle is 5.6 cm. Then what will be the length of its longest chord?

Q. There are two concentric circles with centre O.AD is a chord of a larger circle intersecting the smaller circle at B and C. Prove that AB=CD...

Q.

In how many parts a chord divides a circle?

1. $2$

2. $3$

3. $4$

4. Infinite

Q. 3. Find the area of the segment of a circle whose radius is 10cm and the angle subtended by the corresponding chord at the center is 30 degree.

Q.

Give a method to find the centre of a given circle ?

Q. Question 2 (ii)
Write True or False. Give reasons for your answers.

(ii) A circle has only finite number of equal chords.