Question

As shown in the diagram two circles with radi 8 and 18 touch each other externally and two lines are
tangent of both circles The distance from the intersection of these lines to the centre of the circle with
radius 8 Is​

Answer 1

Answer:

it is the theorem of class 10 and is 10.1.4

Answer 2

Concept:

The tangent line is perpendicular to the radius from the circle's centre to the point of tangency.

Given:

Two circles of radius 8 cm and 18 cm.

Two lines are tangent to both the circles.

Find:

The distance from the intersection of these lines to the centre of the circle with radius 8 cm.

Solution:

Let the centres of the circles be A and B as shown in the diagram below.

In ΔIOA and ΔJOB,

sinθ $=\frac{8}{x+8}=\frac{18}{18+8+8+x}$

(∵ sinθ$\frac{Perpendicular}{hypotenuse}$)

$\frac{8}{x+8}=\frac{18}{18+8+8+x}$

$\frac{8}{x+8}=\frac{18}{34+x}$

$18(x+8)=8(34+x)$

$18x+144=272+8x$

$18x-8x=272-144$

$10x=28$

$x=2.8cm$

The distance from the intersection of these lines to the centre of the circle with radius 8 cm = Distance of OA

Distance of OA $=x+8$

Distance of OA $=2.8+8$

Distance of OA $=10.8cm$

∴ The distance from the intersection of these lines to the centre of the circle with radius 8 cm is 10.8 cm.