Question

If you draw a triangle and draw two circles, one circumscribing the polygon with radius R
and one inscribing the polygon. What is the ratio of the radii of the two circles? (Inscribed to
Circunscribed)
O 3
O 1/3
O 1/2
O 1​

Answer 1

Given : draw a triangle and draw two circles, one circumscribing the polygon with radius R and one inscribing the polygon.

To Find :   ratio of the radii of the two circles (Inscribed to Circumscribed )

O 3

O 1/3

O 1/2

O 1​

Solution:

ratio of the radii of the two circles (Inscribed to Circumscribed )  is not fixed and depends upon triangle

But if Triangle is Equilateral Triangle  with side a

Then  

Radius of Inscribed circle =  a/2√3

Radius of Circumscribed circle =  a/√3

ratio of the radii of the two circles (Inscribed to Circumscribed )  =  ( a/2√3)/( a/√3)

= 1/2

ratio of the radii of the two circles (Inscribed to Circumscribed )  = 1/2 if Triangle is regular polygon ( means Equilateral triangle)

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