المسألة رقم "خمسة"

C1: (x-5)²+(y-5)²=5²
C2: (x-r)²+(y-r)²=r²
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C1 & x = y
x1=-sqrt(5²/2)+5=-5/sqrt(2)+5
y1=x1
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(x1,y1) in C2
(x1-r)²+(y1-r)²=r²
r=x1*sqrt(2)/(1+sqrt(2))
r=5(sqrt(2)-1)/(sqrt(2)+1)
r=5(sqrt(2)-1)²
r=15-10sqrt(2)=0.857864376269049