Question

In a equilateral triangle the
in radius circum radius and one of the ex radii are in the ratio

Answer 1

Answer:

Please see the attachment

Answer 2

Given:

Case of Equilateral Triangle and

Angle A = Angle B= Angle C = 60° and

When a triangle is circumscribed in a circle the circum radius be 'R' and one ofthe external radius as r.

But-:

R = r (as they are the same radius)

So-:

To find out the ratio between the circum radius and the external radius we can use the formula for external radius.

The formula of external radius is

=> 4*RSinA/2*cosB/2*cosC/2

On putting all the values-:

=> 4R*sin 60/2*cos 60/2*cos 60/2

=> 4R*1/2*(3^1/2)/2*(3^1/2)/2

=> 3/2R

Now the resulting ratio we get is -:

=> R:3/2R

=> (2:3)