Perpendicular from the Center to a Chord Bisects the Chord

Q. Two parallel chords are drawn on either side of the centre of a circle of diameter 30 cm. If the length of one chord is 24 cm and the distance between the two chords is 21 cm, then find the length of another chord.
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Q.

In the figure; P and Q are the points of intersection of two circles with centres O & O'. If straight line APB and CQD are parallel to OO', then what is the ratio of OO' and AB?

1. 1:3

2. 1:2

3. 1:4

4. 3:4

Q.

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

1. 28
2. 24
3. 32

4. 30

Q.

Ram says that two chords are at equal distance from centre but the chords are not equal to each other. Is the statement stated by him true or false?

1. True

2. False

Q.

What is the relation between AM and MB in the given figure?

1. 1:4

2. 1:1

3. 1:2

4. 1:3

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. Both statements are true.

4. S1 is true & S2 is false.

Q.

In the figure given below: OA, OB or OC is the _______ of the circle.

1. chord
2. arc
3. secant
4. radius

Q.

An equilateral triangle ABC, whose side is 6 cm, is inscribed in a circle. Find the radius of the circle.

1. $2\sqrt{3}\text{cm}$

2. $2\sqrt{2}\text{cm}$

3. $3\sqrt{3}\text{cm}$

4. $3\text{cm}$

Q.

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

1. 1 : 1

2. 1 : 2

3. 1 : 4

4. 1 : 3

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. 10 cm

2. 11 cm

3. 6 cm

4. 8 cm