Theorem on Touching Circles

Q. Question 11
In figure , O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 and OT intersect the circle at E, if AB is the tangent to the circle at E, find the length of AB.

Q.

Three circles touch each other externally. The distance between their centres is $5cm,6cm$ and $7cm.$ Find the radii of the circles.

1. 1 cm, 2 cm, 4 cm

2. 2 cm, 3 cm, 4 cm

3. 3 cm, 4 cm, 1 cm

4. 1 cm, 2.5 cm, 3.5 cm

Q.

The radius of any circle touching the lines $3x-4y+5=0$and $6x-8y-9=0$is

1. $1.9$

2. $0.95$

3. $2.9$

4. $1.45$

Q. If radii of two circles are 4 cm and 2.8 cm. Draw figure of these circles touching each other – (i) externally (ii) internally.

Q. In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm The diameter of the circle with centre O’ is 10cm. What is the length of the tangent PC?

1. 25 cm
2. 26 cm
3. 24 cm
4. 27 cm

Q. Question 11
In figure , O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 and OT intersect the circle at E, if AB is the tangent to the circle at E, find the length of AB.

Q. Radii of 2 circles are 10 cm and 4 cm respectively. Find the distance between their centres if they touch internally.
[3 Marks]

Q. Two circles having radii $3.5cm$ and $4.8cm$ touch each other internally. Find the distance between their centres.

Q. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. Find the length of the chord CD which is parallel to XY and at a distance of 8 cm from A.

Q.

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of $25cm$ from O as shown in the figure. The radius of the circle with centre O is $7cm$. The diameter of the circle with centre O’ is $10cm.$ What is the length of the tangent PC?

1. $24cm$

2. $25cm$

3. $26cm$

4. $27cm$

Q.

Two circles of radii $13cm$ and $5cm$ touch each other internally. The distance between their centers is $8cm.$

1. 12 cm

2. 18 cm

Q. If two circles with radius a cm and b cm meet externally., then the distance between their centres is equal to ______ cm.

1. $a+b$
2. $a\times b$
3. $\frac{a}{b}$
4. $a-b$

Q.

With the vertices of $△ABC$ as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles. [4 MARKS]

Q.

Radii of 2 circles are 16 cm and 8 cm. Find the distance between their centres if they touch internally.

1. 8 cm

2. 2 cm

3. 4 cm

4. 24 cm

Q. Three circles touch each other externally. The distance between their centres is $5cm,6cm$ and $7cm.$ Find the radii of the circles.

Q. Three circles touch each other externally. The distance between their centres is $5cm,6cm$ and $7cm.$ Find the radii of the circles.

Q.

With the vertices of $△$ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

Q. Two circles which are not congruent touch externally. The sum of their areas is 130$\mathrm{\pi }$ cm² and the distance between the centres is 14 cm. Find the radii of the circles.

Q. The radius of the inner circle of triangle is $4cm$ and the segment into which one side is divided by the point of contact are $6cm$ and $8cm$ determine the other two sides of the triangle.

Q.

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10cm. What is the length of the tangent PC?

1. 25 cm

2. 24 cm

3. 26 cm

4. 27 cm

Q. Two circles of radii $13cm$ and $5cm$ touch each other internally. The distance between their centres is _____.

1. 6 cm
2. 7 cm
3. 18 cm
4. 8 cm

Q. In fig., two concentric circles of radii $a$ and $b(a>b)$ are given. The chord $AB$ of larger circle touches the smaller circle at $C$. The length of $AB$ is:

1. $\sqrt{a^2+b^2}$
2. $2\sqrt{a^2-b^2}$
3. $\sqrt{a^2-b^2}$
4. $2\sqrt{a^2+b^2}$

Q. In triangle PQR, PQ = 24 cm, QR = 7 cm and <PQR = 90°. Find the radius of the inscribed circle. [4 marks]

Q.

With the vertices of $△$ABC as centers, three circles are described, each touching the other two externally. If the sides of the triangle are 7 cm, 8 cm and 11 cm, find the radii of the three circles.

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

1. False
2. True

Q.

Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.

1. 2 cm, 3 cm, 4 cm

2. 3 cm, 4 cm, 1 cm

3. 1 cm, 2.5 cm, 3.5 cm

4. 1 cm, 2 cm, 4 cm

Q. When two circles neither touch nor intersect and one lies outside the other, then four common tangents can be drawn.

1. False
2. True