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)