Question Number 10435 by Joel575 last updated on 09/Feb/17

Commented byJoel575 last updated on 09/Feb/17

The side length of the square is 1 cm.  5 circles have same radius.  What is the value of the circle′s radius?

Answered by sandy_suhendra last updated on 09/Feb/17

Commented bysandy_suhendra last updated on 09/Feb/17

let AC=GB=x and CD=CF=FG=r    so AD=AE=x−r        FB=EB=x+r  AE+EB=1  x−r+x+r=1 ⇒ x=(1/2)  AC=x=(1/2) and CB=2r+x=2r+(1/2)  Phytagoras theorem :  AC^2 +CB^2 =AB^2   ((1/2))^2 +(2r+(1/2))^2 =1^2   (1/4)+4r^2 +2r+(1/4)=1  4r^2 +2r−(1/2)=0  8r^2 +4r−1=0  r = ((−4±(√(16+32)))/(16))  r = ((−4+4(√3))/(16)) = ((−1+(√3))/4)  (r must be positive)