Name: Two Circles Touching Internally and Externally
Uploaded: 2019-07-19
Duration: 6 min 6 s
Description: In this video, we will learn the condition for two circles touching internally and externally using an interesting example. Come, let's learn and watch this...

Question

The length of the radii of two circles are

8 cm

and

3 cm

, the distance between the centres is

13 cm

. What is the length of the direct common tangent of the two circles?

Accepted Answer

Given: $B Q = 8 cm$ , $A P = 3 cm$ and $A B =$ $13 cm$ .

The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference.

$∴ ∠ B Q P = 90 °$

Construct a line segment $A C$ parallel to $P Q$ .

Thus, $∠ A C B = ∠ B Q P = 90 °$ and $B C = B Q - A P = 8 cm - 3 cm = 5 cm$

Therefore, $△ A C B$ is a right-angled triangle.

Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

$∴ A B^{2} = A C^{2} + B C^{2}$

$\Rightarrow 13^{2} = A C^{2} + 5^{2}$

$\Rightarrow A C^{2} = 169 - 25$

$\Rightarrow A C = \sqrt{144}$

$\Rightarrow A C = 12$

Thus, $P Q = A C = 12 cm$

Hence, the length of the direct common tangent of the two circles is $12 cm$ .

The length of the radii of two circles are $8 cm$ and $3 cm$ , the distance between the centres is $13 cm$ . What is the length of the direct common tangent of the two circles?

Important Questions on Theorems Regarding Tangent to a Circle

Learn and Prepare for any exam you want !

The length of the radii of two circles are 8 cm and 3 cm, the distance between the centres is 13 cm. What is the length of the direct common tangent of the two circles?

Important Questions on Theorems Regarding Tangent to a Circle

Learn and Prepare for any exam you want !

The length of the radii of two circles are $8 cm$ and $3 cm$ , the distance between the centres is $13 cm$ . What is the length of the direct common tangent of the two circles?