Quarter circle

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

Correct answer:

r =  41.4214 cm

Step-by-step explanation:

$$\begin{gathered} R=100\text{ cm } \\ {r}^2+r^2=(R-r{)}^2 \\ 2r^2=(R-r{)}^2 \\ \sqrt{2}r=R-r \\ \sqrt{2}r+r=R \\ r(\sqrt{2}+1)=R=100 \\ r=R\mathrm{/}(\sqrt{2}+1)=100\mathrm{/}(\sqrt{2}+1)=41.4214\text{ cm} \end{gathered}$$

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Math student

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

2 years ago  Like

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