Equal Chords of a Circle Are at Equidistant from the Center

Q.

Prove that, of any two chords of a circle, the greater chord is nearer to the centre.

Q.

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .

1. 3 cm

2. 6 cm

3. 8 cm

4. 4 cm

Q. if two equal chords of a circle intersect within the circle, prove that the segements of one chord are equal to corresponding segments og the ot

Q.

Which of the following is incorrect?

1. The perpendicular drawn from the centre of the circle to a chord bisects the chord.

2. Congruent arcs of a circle subtend equal angles at the centre.

3. Congruent arcs of a circle subtend right angles at the centre.

4. Chords equidistant from the centre of a circle are equal in length.

Q.

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

1. 4cm, 4cm

2. 4cm, 8cm

3. 8cm, 8cm

4. 8cm, 4cm

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. rectangle.

3. kite.

4. rhombus.

Q. Equal chords are equidistant from the centre of circle.

1. False
2. True

Q.

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

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. Construct line segment OL such that it bisects chords AB and CD perpendicularly at point L and M respectively.
Find the radius of the circle. (2 marks)

Q.

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

Q.

The perpendicular distance from the centre of a circle to chords of equal length will be ___

1. depends on the chord

2. equal

3. unequal

4. depends on the radius of circle

Q.

If two equal chords are drawn on a circle then they are equidistant from the centre of circle.

1. True

2. False

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.

Which of the following is incorrect?

1. The perpendicular drawn from the centre of the circle to a chord bisects the chord.

2. Congruent arcs of a circle subtend equal angles at the centre.

3. Congruent arcs of a circle subtend right angles at the centre.

4. Chords equidistant from the centre of a circle are equal in length.

Q.

The figure below shows a circle centered at O and of radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. AP is perpendicular to BC. Find the length of the chord BC.

1. 10.6 cm

2. 11.6 cm

3. 5.6 cm

4. 9.6 cm