Name: Tangents From an Exterior Point: Illustration
Uploaded: 2019-07-19
Duration: 4 min 47 s
Description: If you lift a circular object with a pair of tongs, then the tongs are two tangents to the circular object. Let us study the properties of tangents drawn fro...

Question

Two concentric circles are of radii

5 cm

and

3 cm

. Find the length of the chord of larger circle which touches the smaller circle.

Accepted Answer

According to question, the figure is as follows

Here, radius of smaller circle, $r = 3 cm$

and, radius of larger circle, $R = 5 cm$

We have to find the length of chord $A C$

Here, $A C = A B + B C$

$A C$ is a chord for larger circle, but it is tangent for smaller circle.

$∴ ∠ O B A = 90 °$ [ $∵$ Angle between tangent to a point on circle and radius from same point makes an angle of $90 °$ ]

Hence, $A B O$ is a right angled triangle.

Apply Pythagoras theorem in $△ A B O$

i.e. $A O^{2} = A B^{2} + B O^{2}$

$\Rightarrow R^{2} = A B^{2} + r^{2}$

$\Rightarrow A B^{2} = R^{2} - r^{2}$

$\Rightarrow A B^{2} = \sqrt{25 - 9} = \sqrt{16}$

$\Rightarrow A B = 4 cm$

Hence, length of $A C = 2 \times A B$

$= 2 \times 4$

$= 8 cm$

Thus, length of chord of larger circle is $8 cm$

Two concentric circles are of radii $5 cm$ and $3 cm$ . Find the length of the chord of larger circle which touches the smaller circle.

Important Questions on Circles

Learn and Prepare for any exam you want !

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of larger circle which touches the smaller circle.

Important Questions on Circles

Learn and Prepare for any exam you want !

Two concentric circles are of radii $5 cm$ and $3 cm$ . Find the length of the chord of larger circle which touches the smaller circle.