A Line through the Center That Bisects the Chord Is Perpendicular to the Chord

Q. In the given figure, the line segment is the diameter of the circle.

1. OA
2. EC
3. AB
4. AD

Q.

In an equilateral $△$ABC inscribed in a circle, the perpendicular bisector of BC & the angle bisector of angles B & C meet at the centre of the circle.

1. True
2. False

Q.

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

1. None of these

2. 23 cm

3. 30 cm

4. 15 cm

Q. In the given figure O is the centre of the circle with radius 10 cm. OP and OQ are perpendiculars to AB and CD respectively. Determine the value of PQ if AB = 16 cm and CD = 12 cm.

1. 10cm
2. 14cm
3. 13cm
4. 12cm

Q.

AB is a chord of a circle with centre O and $\angle x={90}^{\circ }$

1. 90°

2. 80°

Q. Find the measure of AP, if CD = 24cm

1. 12cm
2. 6cm
3. 8cm
4. 10cm

Q.

In an equilateral $△$ABC inscribed in a circle, the perpendicular bisector of BC & the angle bisector of angles B & C meet at the center of the circle.

1. True

2. False

Q.

AB is a chord of a circle with centre O.
The chord is bisected at the foot of the perpendicular.

Hence, $\angle x={90}^{\circ }$

1. 80°

2. 90°

Q. If two equal chords of a circle intersect, then prove that their segments are equal.
$\left[3Marks\right]$

Q.

The line drawn through the centre of a circle to bisect a chord is __ to the chord.

Q. 39. The circular wire diameter10 cm is cut and placed along the circumference of a circle of diameter 1m . The angle subtended by the wire at the center equal to 1./4 2./3 3./5 4./10

Q. AD is a diameter of a circle and AB is a chord If AD = 34 cm, AB = 30 cm the distance of AB from the centre of the circle is

1. 17 cm
2. 15 cm
3. 4 cm
4. 8 cm

Q.

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

1. 3 cm

2. 4 cm

3. 5 cm

4. 3.5 cm

Q.

Draw and describe the locus in each of the following cases:

(iv) The locus of centres of all circles passing through two fixed points.

Q.

How many circles can be drawn circumscribing a given triangle?

1. infinite

2. 1

3. 2

4. 3

Q. The line drawn from the centre of the circle to bisect the chord at ____ degrees.

1. 270
2. 180
3. 90
4. 360

Q. Two chords of lengths 16 cm and 17 cm are drawn perpendicular to each other in circle of radius 10 cm. The distance of their point of intersection from the centre is approximately

1. 6.5 cm
2. 7.6 cm
3. 7.2 cm
4. 8 cm