Perpendicular from the Center to a Chord Bisects the Chord

Q.

Two equal circles of radius r intersect such that each passes through the centre of the other. The length of the common chord of the circles is

1. $\sqrt{r}$

2. $\sqrt{2}rAB$

3. $\sqrt{3}r$

4. $\frac{\sqrt{3}}{2}r$

Q. Find the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm.

Q.

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is

1. 15 cm

2. 34 cm

3. 16 cm

4. 17 cm

Q.

In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is:

1. 2AB

2. √2 AB

3. 1/2AB

4. (1/√2)AB

Q.

Find the length of a chord which is at a distance of $5cm$ from the center of a circle of radius $10cm.$

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. The radius of the circle is

1. $5\sqrt{2}cm$

2. $3\sqrt{5}cm$

3. 6 cm

4. 7 cm

Q.

Two chords $AB,$ $CD$ of lengths $5cm$ and $11cm$ respectively of a circle are parallel. If the distance between $AB$ and $CD$ is $3cm,$ find the radius of the circle.

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. $\sqrt{5}cm$

2. $2\sqrt{5}cm$

3. $2\sqrt{7}cm$

4. $\sqrt{7}cm$

Q.

The length of two parallel chords of a circle are $6$ cm and $8$ cm. If the smaller chord is at a distance of $4$ cm from the centre, what is the distance of the other chord from the centre ?

Q.

A circular park of radius $40m$ is situated in a colony. Three boys Ankur, Amir, and Anand are sitting at an equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.

Q.

If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.

Q.

In a circle of radius 17 cm, two parallel chords are drawn on opposite side of a diameter. This distance between the chords is 23 cm. If the length of one chord is 16 cm then the length of the other is

1. 23 cm

2. 30 cm

3. 15 cm

4. 34 cm

Q. Radius of a circle with centre O is 41 units. Length of a chord PQ is 80 units, find the distance of the chord from the centre of the circle.

Q.

Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius $20m$ drawn in a park. Ishita throws a ball to Isha, Isha to Nisha and Nisha to Ishita. If the distance between Ishita and Isha and between Isha and Nisha is $24m$ each, what is the distance between Ishita and Nisha?

Q.

Two concentric circles are of radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.

Q. The area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. Length of one parallel sides is 84cm. The length of other is

1. 38 cm
2. 28 cm
3. 18 cm

Q.

A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is

1. 12 cm

2. 18 cm

3. 16 cm

4. 14 cm

Q.

In the given figure, AB is chord of a circle with centre O and BOC is a diameter. If OD$\perp$AB such that OD = 6 cm then AC = ?

(a) 9 cm

(b) 12 cm

(c) 15 cm

(d) 7.5 cm

Q.

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.

Q.

In the given figure, CD is the diameter of a circle with centre O and CD is perpendicular to chord AB. If AB = 12 cm and CE = 3 cm then radius of the circle is

(a) 6 cm

(b) 9 cm

(c) 7.5 cm

(d) 8 cm

Q. Construct $∆$ PQR such that $\angle$P = ${70}^{°}$ , $\angle$R = ${50}^{°}$ , QR = 7.3 cm and constructs its circumcircle.

Q.

O is the circumcentre of the triangle ABC and OD is perpendicular on BC, Prove that $\angle BOD=\angle A$

Q. If the chord y = mx + 1 of the circle $x^2+y^2=1$ subtends an angle of measure ${45}^{\circ }$ at the major segment of the circle then value of m is

1. 2
2. -2
3. -1
4. none of these

Q.

Suppose you are given a circle. Give a construction to find its centre.

Q.

Question 3
The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Q.

In the adjoining figure, $OD$ is perpendicular to the chord $AB$ of a circle with centre $O$. If $BC$ is a diameter, show that $AC||DO$ and $AC=2\times OD$.

Q.

ABC is a triangle with B as right angle, AC = 5 cm and AB = 4cm. A circle is drawn with O as centre and OC as radius. The length of the chord of this circle passing through C and B is

1. 3 cm

2. 4 cm

3. 5 cm

4. 6 cm

Q.

Find the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm.

Q.

In the given figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is

(a) 10 cm

(b) 12 cm

(c) 6 cm

(d) 8 cm

Q.

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