# Find the area of the blue shaded region...

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A circle is inscribed in a square as shown in figure. A smaller circle is drawn tangent to two sides of the square and externally tangent to the inscribed circle. Find the area of the blue shaded region...

posted Jun 8, 2016

2(5-r)²= (5+r)²
√2 (5-r) = 5+r
5√2 - √2.r = 5+r
(1+√2)r =5√2 - 5
R = (5√2 - 5)/(1+√2)
The area of the shaded space is
5²-(25pi/4)-((5√2-5/1+√2)²pi)

answer Feb 20, 2017 by anonymous

The problem lies in finding the small circle area; since its radius doesn't start from the square corner, we cannot just subtract the Bigger circle radius from the square diameter and divide by 2.

The solution i came with is finding the ratio between (the the bigger circle radius) and (the part of the diameter that is crossing over the blue shaded area + circle radius)...
.
This will let us know how to calculate the small circle radius by knowing only the length of the line that is crossing over the blue shaded area.

.
So the shaded section area (inlc small circle) :
(10*10-pi*5^2)/4)

-
small circle area:
pi*(((5sqrt(2)-5)-(5sqrt(2)-5)*(5sqrt(2)-5)/(10+(5sqrt(2)-5)))/2)^2

=
3.053
.

This is the calculation I came up with:
http://bit.ly/2mbAFqt

answer Feb 24, 2017 by anonymous

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