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

Q.

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

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.

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

1. 90°

2. 80°

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

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

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

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.

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. The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CD = 32 cm and EB = 4 cm, then find the radius of the circle.
[4 Marks]