Tangent and Secant

Q.

Two chords AB and CD of a circle intersect each other at P outside the circle. If AB = 5 cm, BP = 3 cm and PD = 2cm, find CD

Q.

In the given fig, find the perimeter of $\Delta$ABC, if AP = 10 cm

Q.

In the given figure if 'O' is the centre of the circle then $\angle AOB$ =___

Q.

In the figure, AB is the common tangent to the 2 circles intersecting at C & D. Write down the numerical value of ∠ACB + ∠ADB. Give reasons for your answer.

1. 180^o

2. 270^o

3. 360^o

4. 120^o

5. 90^o

Q. Maximum number of common tangents that can be drawn for two externally touching circles = .

1. 1
2. 3
3. 4
4. 2

Q. If AB is a tangent to a circle at B and ACD any other chord then ABsquare=ACAD.

Q.

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, Calculate the radius of the circle.

1. 12.25 cm

2. 11.25 cm

3. 13.95 cm

4. 21.10 cm

Q. In case of two circles touching each other externally, three common tangents can be drawn to the circles.

1. False
2. True

Q.

In the figure; AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If $\angle C={20}^0$, find $\angle AOD$

1. ${60}^o$

2. ${50}^o$

3. ${120}^o$

4. ${90}^o$

Q.

In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD=7.8 cm, PD = 5 cm, PB = 4 cm. Select the statements that are true.

1. PT = 2 cm

2. AB = 12 cm

3. PT = 8 cm

4. AB = 9 cm

Q. The region bound by a chord and the arc of the circle is called segment

1. True
2. False

Q.

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

1. 10cm

2. 15cm

3. 20cm

4. 25cm

Q.

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

1. 10cm

2. 15cm

3. 20cm

4. 25cm

Q.

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

1. 15 cm

2. 20 cm

3. 10 cm

4. 25 cm

Q.

In the figure a chord AB on the circle. If the angle made by AB on the Circumference of the circle is $\angle ACB={55}^{\circ }$. What is the angle $\angle AOB$(in degrees)?

1. 110

2. 55

3. 210

4. 90

Q.

The maximum number of common tangents that can be drawn for two externally touching circles is/are ___.

Q. A secant passes through ____ points.

1. 1
2. 2
3. 3
4. 4

Q. if two circles touch each other externally , then the number of common tangents are

Q.

All circles are _________ to each other.

1. congruent

2. similar

Q.

A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.

1. 10 cm

2. 15 cm

3. 20 cm

4. 25 cm

Q. Sector is the region between a chord and its corresponding arc.

1. True
2. False

Q. Assertion (A)
At point P of a circle with centre O and radius 12 cm, a tangent PQ of length 16 cm is drawn. Then, OQ = 20 cm.

Reason (R)
The tangent at any point of a circle is perpendicular to the radius through the point of contact.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Q. Using the jumbled letters, identify the part of the circle which is common in all these images.

1. 
2. 
3. 
4. 

Q. Sector is the region between a chord and its corresponding arc.

1. False
2. True

Q.

if 2 circled touch each other externally then the number of common tangents are------

-4

-3

-2

-1

Q. In case of two circles touching each other externally, three common tangents can be drawn to the circles.

1. False
2. True

Q. Calculate the circumference of a circle that has a radius of 14 cm.

Q.

In the fig., AB is a diameter of the circle C(O, r) and radius OD is perpendicular to AB. If C is any point on arc DB, find ∠BAD and ∠ACD.

Q. All circles are _________ to each other

1. Congruent
2. Similar

Q. Using the jumbled letters, identify the part of the circle which is common in all these images.

1. 
2. 
3. 
4.