plotting - Finding a point from a set of contours such that it is nearest to a given point

I have several contour lines and one point. How can I find a point in one of those contour lines which is nearest to the given point?

(*Create the implicit curves*)
Data={{10,20,1},{10,40,2},{10,60,3},{10,80,4},{20,25,2},{20,45,3},{20,65,4},{30,30,3},{30,50,4},{40,35,4},{40,55,5},{50,20,4},{50,40,5},{60,25,5}};
U=NonlinearModelFit[Data,a x^b (y^(1-b))+c,{a,b,c},{x,y}];
L={ContourPlot[U[x,y]=={1},{x,0,100},{y,0,100},ContourStyle->Red],ContourPlot[U[x,y]=={2},{x,0,100},{y,0,100},ContourStyle->Magenta],ContourPlot[U[x,y]=={3},{x,0,100},{y,0,100},ContourStyle->Brown],ContourPlot[U[x,y]=={4},{x,0,100},{y,0,100},ContourStyle->Blue],ContourPlot[U[x,y]=={5},{x,0,100},{y,0,100},ContourStyle->Green]};
(*Point nearest to which we need to find the points on the curves*)
pt={30,50};

(*Graphic*)
Show[L,Graphics[{PointSize[Large],Blue,Point[pt]}],FrameLabel->{"X","Y"}]

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front end - keyboard shortcut to invoke Insert new matrix

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