Theorem 4:Equal Chords Are at Equal Distance from the Center

Q.

If I draw a circle on a tracing paper and draw two equal chords and drop perpendicular from centre to the chord. Fold the paper such that the two chords coincide. Then, the two perpendiculars are also coinciding.

1. True

2. False

Q.

Question 3
If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Q.

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 12 cm, PC = 4 cm, then find the length of chord CD.

Q.

Two equal chords, $AB$ and $CD$ are at a distance of 10 cm from each other. Find the distance of chord $AB$ from the centre.

1. $6cm$

2. $5cm$

3. $12cm$

4. $20cm$

Q.

In a circle of radius 5 cm and centre O, AB and AC are two chords such that AB = AC = 6 cm. AO is the perpendicular bisector 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

Q.

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 10 cm, PC = 5 cm, then the length of chord CD is

1. Can't be determined

2. 60°

3. 20°

4. 50°

Q.

Two equal chords, $AB$ and $CD$ are at a distance of 10 cm from each other. Find the distance of chord $AB$ from the centre.

1. $5cm$

2. $20cm$

3. $6cm$

4. $12cm$

Q. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle.

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 a circle of radius 5 cm, $AB$ and $AC$ are two chords such that $AB=AC=6cm.$ Find the length of the chord $BC$.

1. 9.6 cm

2. 10.6 cm

3. 11.6 cm

4. 5.6 cm

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.

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.

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. 8cm, 4cm

2. 8cm, 8cm

3. 4cm, 4cm

4. 4cm, 8cm

Q.

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

1. True

2. False

Q. Which of the following is/are correct?

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. Question 11
Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB = PD.