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Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

 May 19, 2024
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avatar+14968 
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Find WX.

 

\(h_{yz}=\sqrt{r^2-2^2}\\ h_{uv}=\sqrt{r^2-3^2}\\ h_{yz}-h_{uv}=2\\ \sqrt{r^2-2^2}-\sqrt{r^2-3^2}=2\\ r=\frac{\sqrt{145}}{4}=3.0104\ (WolframAlpha)\)

\(h_{yz}=2.25\\ h_{uv}=0.2500\\ h_{wx}=(2.25+0.250)/2=1.25\\ \overline{WX}=2 \sqrt{r^2-h_{wx}^2}=2\sqrt{3.0104^2-1.25^2}\\ \color{blue}\overline{WX}=5.4772\)

 

laugh !

 May 19, 2024

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