Plotting point on a curve and a circle. Then, connect those points

Question

I have a curve and a circle on x,y axes. I want to plot points on the curve and on the circle based on the "a". The value of "a" should be {1/5,2/5,3/5,4/5} of the curve and the circle. Then, I want to connect those points on curve and the circle. I've been working on this for several days but still couldn't found the solution.

Quad1 = {{-1, 0}, {0, 1}, {1, 0}};(*Define 3 control points for the polygon*) Print[MatrixForm[Quad1]] q1 = Graphics[BezierCurve[Quad1]]; (*Construct a Bezier Curve*) a = BezierFunction[Quad1] Show[Graphics[{Red, Point[Quad1], Green, Line[Quad1]}, Axes -> True], ParametricPlot[a[t], {t, 0, 1}], ParametricPlot[{{ Cos[t], Sin[t]}}, {t, 0, Pi}, PlotLegends -> "Expressions", PlotStyle -> Orange, PlotRange -> {0, 1}]] a1 = a[1/5] a2 = a[2/5] a3 = a[3/5] a4 = a[4/5]

Answer 1

Quad1 = {{-1, 0}, {0, 1}, {1, 0}};

a = BezierFunction[Quad1];

pts1 = a /@ Range[1/5, 4/5, 1/5];

pts2 = {Cos[#], Sin[#]} & /@
   (Pi Range[4/5, 1/5, -1/5]);

Show[
 ParametricPlot[{Cos[t], Sin[t]}, {t, 0, Pi}],
 ParametricPlot[a[t], {t, 0, 1}],
 Epilog -> {
   AbsolutePointSize[6],
   Green,
   Line[Quad1],
   Red,
   Point[pts1],
   Point[pts2],
   Dashed,
   Line /@ Transpose[{pts1, pts2}]}]