Intersecting Chord Properties Both Internally and Externally

Q.

A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.

1. ${150}^{\circ },{30}^{\circ }$

2. ${120}^{\circ },{60}^{\circ }$

3. ${30}^{\circ },{150}^{\circ }$

4. ${60}^{\circ },{120}^{\circ }$

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.

In the figure, $\angle ADC={130}^{\circ }$ and chord $BC=$ chord $BE.$ Find $\angle CBE$

Q.

In the given figure, chords AB and CD when extended meet at P. If AB = 4 cm, BP = 6 cm, DP = 5 cm, then CD =__.

1. 12 cm
2. 10 cm
3. 8 cm
4. 7 cm

Q. ABCD is a cyclic quadrilateral. If the length of AB, BC, CD and AD are 8, 6, 7, and 5 cm respectively, then AC$\times$BD = .

1. 86 ${cm}^2$
2. 56 ${cm}^2$
3. 48 ${cm}^2$
4. 96 ${cm}^2$

Q. Two chords PQ and RS intersect at point O inside the circle. If OP = 4 cm, OQ = 9 cm and RS = 12 cm, then the value of OR is .

1. 5 cm
2. 6 cm
3. 7 cm
4. 8 cm

Q.

Find the value of CD?

Q.

Find the value of CD?

1. 4 cm

2. 6 cm

3. 9 cm

4. 12 cm

Q. A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and also at a point on the minor arc.

1. ${30}^{\circ },{150}^{\circ }$
2. ${150}^{\circ },{30}^{\circ }$
3. ${120}^{\circ },{60}^{\circ }$
4. ${60}^{\circ },{120}^{\circ }$

Q. Let ABCD be a cyclic quadrilateral with sides AB = 2 cm, BC = 7 cm, CD = 11 cm, DA = 14 cm. Find the product of its diagonals.

1. 120 cm
2. 125 cm
3. 34 cm
4. 364 cm

Q. Let ABCD be a cyclic quadrilateral with sides AB = 2 cm, BC = 7 cm, CD = 11 cm, DA = 14 cm. Find the product of its diagonals.

Q. A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .

Q. A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc.

Q.

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

1. 4.8 cm

2. none of these

3. 10.8 cm

4. 9.6 cm

Q. A chord AB of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc and minor arc respectively .

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. 5.6 cm

2. 9.6 cm

3. 10.6 cm

4. 11.6 cm

Q. Two chords PQ and RS intersect at point O inside the circle. If OP = 4 cm, OQ = 9 cm and RS = 12 cm, then find the length of OR.

Q. Let ABCD be a cyclic quadrilateral with sides AB = 2 cm, BC = 7 cm, CD = 11 cm, DA = 14 cm. Find the product of its diagonals.

1. 125 cm
2. 120 cm
3. 364 cm
4. 34 cm

Q. The radii of two concentric circles are 17 cm and 10 cm. A line segment PQRS cuts the larger circle at P and S and the smaller circle at Q and R. If QR= 12 cm. The length of PQ is

1. 9 cm
2. 18cm
3. 15cm
4. 8cm

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. 5.6 cm

2. 9.6 cm

3. 10.6 cm

4. 11.6 cm

Q.

Diameter AB and a chord CD intersect internally at P. If PA = 8, PB = 2, then PC =

1. 5

2. 2

3. 3

4. 4

Q.

Find the value of x

1. 46

2. 54

3. 40

4. 56