Find the radius of the equal 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
We have three equal circles. Suppose the radius of each circle is equal to \(r\).
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