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.
Find WX
U(−3,0),V(3,0),Y(−2,2),Z(2,2)UY(−2.5,1)m=yY−yUxY−xU=2−0(−2)−(−3)m=2
f(x)=m(x−xU)+yU=2(x−(−3))+0f(x)=2x+6f(xM)=−1m(x−xUY)+yUY=−12(x−(−2.5))+1f(xM)=−0.5x−0.25x=0M(0,−0.25) , Center of the enclosing circle
r=√xZ 2+(yZ−yM)2=√22+(2−(−0.25))2r=3.0104 , Radius of the enclosing circle
fcirc(x)=yM±√r2−x21=−0.25+√3.01042−x2(1+0.25)2=3.01042−x2xWX=±√3.01042−1.252xWX=±√7.5=±2.7386¯WX=5.4772
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