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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 13, 2025
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Find WX

 

U(3,0),V(3,0),Y(2,2),Z(2,2)UY(2.5,1)m=yYyUxYxU=20(2)(3)m=2

 

f(x)=m(xxU)+yU=2(x(3))+0f(x)=2x+6f(xM)=1m(xxUY)+yUY=12(x(2.5))+1f(xM)=0.5x0.25x=0M(0,0.25) , Center of the enclosing circle

 

r=xZ 2+(yZyM)2=22+(2(0.25))2r=3.0104 , Radius of the enclosing circle

 

fcirc(x)=yM±r2x21=0.25+3.01042x2(1+0.25)2=3.01042x2xWX=±3.010421.252xWX=±7.5=±2.7386¯WX=5.4772

 

laugh !

 May 25, 2025
edited by asinus  May 25, 2025

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