Intersecting Chord Properties of Circle

Q.

AB is the diameter of a circle with centre O. CD is a chord perpendicular to diameter intersecting it at P. Find the length of chord if PA = 2 cm and PB = 4 cm.

1. 2 cm

2. $\sqrt{8}$ cm

3. 4 cm

4. $4\sqrt{2}$ cm

Q. Two chords AB and CD intersect at point P inside the circle. Find PD if PA = 6 cm, PB = 3 cm and PC = 2 cm.

1. 18 cm
2. 7 cm
3. 9 cm
4. 8 cm

Q. Two chords AB and CD intersect at point P inside the circle. Find PD if PA = 6 cm, PB = 3 cm and PC = 2 cm.

1. 7 cm
2. 9 cm
3. 8 cm
4. 18 cm

Q. If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is ${60}^{\circ }$, then find the length of OP.

Q.

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

1. The angle subtended at P and Q by AB are always equal.

2. The angle subtended by AB at P and Q are either equal or supplementary.

3. The sum of the angle subtended by AB at P and Q is always equal two right angle.

4. The sum of the angle subtended at P and Q is equal to four right angles

Q. Two chords AB and CD intersect at point O inside the circle. If OA = 5 cm, OB = 6 cm and OC = 3 cm, then the value of CD is .

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

Q. Two chords AB and CD intersect at point O inside the circle. If OA = 5 cm, OB = 6 cm and OC = 3 cm, then find the value of CD.

Q.

Two tangents PA and PB are drawn to the circle with centre O, such that $\angle$APB =${120}^{\circ }$what is the relation between OP and AP?

1. OP = 2 AP

2. OP = 1/2 AP

3. OP = AP

4. AP = 2 /3 OP

Q.

State whether the following statements are true or false.

A segment is a region bounded by an arc and a chord.

1. True
2. False

Q. A segment of a circle is the region bounded by a and the arc subtended by it.

1. radius
2. chord
3. tangent

Q. The chord that passes through the centre of a circle is called the ______.

1. diameter
2. radius
3. arc
4. tangent