# Theorem on Touching Circles

## Trending Questions

**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 5 cm, 6 cm and 7 cm. Find the radii of the circles.

1 cm, 2 cm, 4 cm

2 cm, 3 cm, 4 cm

3 cm, 4 cm, 1 cm

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

$1.9$

$0.95$

$2.9$

$1.45$

**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?

- 25 cm
- 26 cm
- 24 cm
- 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 3.5 cm and 4.8 cm 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 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 10 cm. What is the length of the tangent PC?

24 cm

25 cm

26 cm

27 cm

**Q.**

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

12 cm

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.

- a+b
- a×b
- ab
- 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.

8 cm

2 cm

4 cm

24 cm

**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.

**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.

**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$\mathrm{\pi}$ cm

^{2}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 4 cm and the segment into which one side is divided by the point of contact are 6 cm and 8 cm 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?

25 cm

24 cm

26 cm

27 cm

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

- 6 cm
- 7 cm
- 18 cm
- 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:

- √a2+b2
- 2√a2−b2
- √a2−b2
- 2√a2+b2

**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.

- False
- 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.

2 cm, 3 cm, 4 cm

3 cm, 4 cm, 1 cm

1 cm, 2.5 cm, 3.5 cm

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.

- False
- True