Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?

Result

r =  41.421 cm

Solution:

R=100 cm r2+r2=(Rr)2 2r2=(Rr)2 2r=Rr 2r+r=R r(2+1)=R=100  r=R/(2+1)=100/(2+1)41.421441.421 cmR=100 \ \text{cm} \ \\ r^2 + r^2=(R-r)^2 \ \\ 2r^2=(R-r)^2 \ \\ \sqrt{ 2 } r=R-r \ \\ \sqrt{ 2 } r+r=R \ \\ r(\sqrt{ 2 }+1)=R=100 \ \\ \ \\ r=R / (\sqrt{ 2 }+1)=100 / (\sqrt{ 2 }+1) \doteq 41.4214 \doteq 41.421 \ \text{cm}



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Math student
Where did the +1 in the r = R / (sqrt(2) + 1) come from?

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