Find the radius of the equal blue circles
Home -> Solved problems -> Find the radius of the blue circles
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Solution
We have two line segments that meet at a right corner like it is shown in the next figure
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We have three equal circles. Suppose the radius of each circle is equal to \(r\).
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Using the right triangle, we get
\[\begin{aligned}
&(1-3 r)^{2}+(1-r)^{2}=(1+r)^{2} \\\\
&1-6 r+9 r^{2}+1-2 r+r^{2}=1+2 r+r^{2} \\\\
&9 r^{2}-10 r+1=0 \\\\
&(9 r-9)(r-\frac{1}{9})=0 \\\\
&r=1 \text { or } r=\frac{1}{9}
\end{aligned}\]
the blue circle’s radius must be smaller than the largest circle’s radius so we can reject the solution \(r= 1\).
Thus,
\[\large \color{blue} {r=\frac{1}{9}}\]
Home -> Solved problems -> Find the radius of the blue circles
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Home -> Solved problems -> Find the radius of the blue circles