In the given figure, the rectangle at the corner measures 1 cm x 2 cm. What is the radius of the circle in cm?

Let   (0,0)  be the  center  of the  circle

The lower right  vertex of the  rectangle  is   ( r -2, r - 1  )

So the distance   from  the  center  to  this point  is   r^2....so  we have

r^2 = ( r-2)^2  + (r-1)^2

r^2  = r^2  - 4r + 4  + r^2 - 2r + 1

r^2 - 6r   +  5   =   0    factor

(r - 5) ( r - 1)  = 0

The  first factor set  =  0     gifes us the radius

r - 5   =   0 

r  = 5 (cm)