Question 1146409
A circle of radius 6 cm is inscribed in a square.
 A smaller circle is drawn tangent to the two sides of the square and the bigger circle.
 What is the radius of the smaller circle?
:
I assume this smaller circle is in the corner of the square
The side of the square is equal to the diameter of circle or 12 cm
Find the diagonal of the square (which passes through smaller circle)
d = {{{sqrt(2(12^2))}}}
d = {{{12sqrt(2)}}}
the diameter of the smaller circle is equal to half the diagonal - the radius of the larger circle
{{{6sqrt(2) - 6}}} = 2.485 cm
radius of the smaller circle then is {{{2.485/2}}} = 1.2425 cm