I want to plot a graph that represents the distance of a moving point on a line and the center of a circle, I want to plot the graph on the right (the red dotted graph)
screenshot of an explanatory image: 
thanks in advance :)
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4 Answers
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DynamicModule[{pointOnLine, list}, Manipulate[ Row[{ LocatorPane[ Dynamic@{endA, endB, center}, Graphics[{ Circle[center, radius], {Dashed, Line[{endA, endB}]}, PointSize[0.02], Point[pointOnLine], {Red, Line[{center, pointOnLine}]} }, PlotRange -> 10, Axes -> False, Frame -> True, ImageSize -> Medium ] ], ListPlot[ list, PlotStyle -> Red, AspectRatio -> 1, Axes -> False, Frame -> True, ImageSize -> Medium ] }], {{center, {3, 1}}, None}, {{endA, {-5, 5}}, None}, {{endB, {0, -5}}, None}, {{radius, 2}, 1, 8}, {{positionAlongLine, 0.3}, 0, 1, Appearance -> "Open", TrackingFunction -> (( positionAlongLine = #; pointOnLine = endB + positionAlongLine (endA - endB); AppendTo[list, {#, EuclideanDistance[center, pointOnLine]}] )&) }, Button["Discard plot points and restart", list = {}], Initialization :> ( list = {}; pointOnLine = endB + positionAlongLine (endA - endB) ) ] ] 
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Manipulate[ Row[{Graphics[{ Red, Circle[{x0, y0}, r] , Dashed, Black , Line[{{x1, y1}, {x2, y2}}] , Line[{{x0, y0}, (1 - t) {x1, y1} + t {x2, y2}}] , Red, AbsolutePointSize[6] , Point[(1 - t) {x1, y1} + t {x2, y2}] , Blue, Point[{x1, y1}] , Point[{x2, y2}] , Darker@Green , Point[{x0, y0}] } , Frame -> True , ImageSize -> 200 , PlotRange -> {{-5, 5}, {-5, 5}} , GridLinesStyle -> {{Gray, Dotted}, {Gray, Dotted}} , GridLines -> Automatic ], , g = RegionDistance[ Point[{x0, y0}], (1 - t) {x1, y1} + t {x2, y2}]; , Plot[ EuclideanDistance[(1 - x) {x1, y1} + x {x2, y2}, {x0, y0}] , {x, 0, 1} , PlotRange -> {{0, 1}, {0, 6}} , ImageSize -> 200 , PlotLabel -> Style[g, Black, 12] , GridLinesStyle -> {{Gray, Dotted}, {Gray, Dotted}} , GridLines -> Automatic , Epilog -> {Red, AbsolutePointSize[6] , Point@{t, g} , Dashed, Black , Line[{{t, g}, {t, 0}}] } ] }] , {{x0, 0}, -1, 1} , {{y0, 0}, -1, 1} , {{r, 2}, 0, 4} , {{x1, 3}, -4, 4} , {{y1, 3}, -4, 4} , {{x2, -4}, -4, 4} , {{y2, -1}, -4, 4} , {{t, 0.5}, 0, 1} , TrackedSymbols :> All ] 
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EuclideanDistance gives the distance between two points. One way to specify a point on your line is
(1-t){a1,b1} + t {a2,b2} which moves between the two endpoints as t goes from 0 to 1. The distance to the center of the circle is
EuclideanDistance[(1-t){a1,b1} + t {a2,b2}, {x0,y0}] Giving numerical values to the endpoints and center, you can then plot this distance to get the distance plot. For example, with endpoints {0,3} and {1,0} and circle center at {3,2} gives
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My goodness... all this code can be eliminated if you recall Pythagoras' Theorem: $d = \sqrt{h^2 + s^2}$ where $h$ is the distance from the circle's center to the nearest point on the line (call it $P$) and $s$ is the distance of the point in question from $P$.
