Still on Filling

Question

I am really sorry to bother you for the same problems, but I cannot get in the view about this command, the filling option.

What I want: to fill the semicircle part, under the $y = x$ curve. Here is what I did so far, but there is a slight piece filled in excess. Can you please tell me how I would proceed?

f[x_] = 1 + Sqrt[1 - (x - 1)^2];
h[x_] = x;
g[x_] = 1 - Sqrt[1 - (x - 1)^2];
Plot[{f[x], g[x], h[x], 
ConditionalExpression[h[x], 0 < x < 2]}, {x, -1, 3}, 
AspectRatio -> Automatic, 
PlotStyle -> {{Darker@Cyan, Dashed}, {Darker@Cyan, 
Dashed}, {Darker@Green, Dashed}, Darker@Green}, 
Filling -> {3 -> {2}}, FillingStyle -> {None, LightRed}, 
PlotRange -> {-1.5, 2.5}, AxesStyle -> Arrowheads[{0.05}], 
GridLines -> {{{-2, {Thick, AbsoluteDashing[{3, 3}]}}}, None}, 
Epilog -> {{AbsoluteThickness[1.75]}, AbsoluteDashing[3, 3], 
Line[{{1 + 1/Sqrt[2], 0}, {1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}}], 
Line[{{1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}, {0, 1 + 1/Sqrt[2]}}]}]

Answer 1

r = RegionPlot[(x - 1)^2 + (y - 1)^2 < 1 && x > y, {x, -1.5, 
    2.5}, {y, -1.5, 2.5}, PlotPoints -> 100, BoundaryStyle -> None, 
   PlotStyle -> LightRed, AxesStyle -> Arrowheads[{0.05}], 
   Axes -> True, Frame -> False];

Show[
 r,
 Plot[{f[x], g[x], h[x], 
   ConditionalExpression[h[x], 0 < x < 2]}, {x, -1, 3}, 
  AspectRatio -> Automatic, 
  PlotStyle -> {{Darker@Cyan, Dashed}, {Darker@Cyan, 
     Dashed}, {Darker@Green, Dashed}, Darker@Green}, 
  PlotRange -> {-1.5, 2.5}], 
 Epilog -> {{AbsoluteThickness[1.75]}, AbsoluteDashing[3, 3], 
   Line[{{1 + 1/Sqrt[2], 0}, {1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}}], 
   Line[{{1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}, {0, 1 + 1/Sqrt[2]}}]}]

Answer 2

Try the following:

f[x_] = 1 + Sqrt[1 - (x - 1)^2];
h[x_] = x;
g[x_] = 1 - Sqrt[1 - (x - 1)^2];
f1 = Plot[{f[x], g[x], h[x], 
    ConditionalExpression[h[x], 0 < x < 2]}, {x, -1, 3}, 
   AspectRatio -> Automatic, 
   PlotStyle -> {{Darker@Cyan, Dashed}, {Darker@Cyan, 
      Dashed}, {Darker@Green, Dashed}, Darker@Green}, 
   Filling -> {3 -> {1}}, FillingStyle -> {None, White}, 
   PlotRange -> {-1.5, 2.5}, AxesStyle -> Arrowheads[{0.05}], 
   GridLines -> {{{-2, {Thick, AbsoluteDashing[{3, 3}]}}}, None}, 
   Epilog -> {{AbsoluteThickness[1.75]}, AbsoluteDashing[3, 3], 
     Line[{{1 + 1/Sqrt[2], 0}, {1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}}], 
     Line[{{1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}, {0, 1 + 1/Sqrt[2]}}]}];
f2 = Plot[{f[x], g[x], h[x], 
    ConditionalExpression[h[x], 0 < x < 2]}, {x, -1, 3}, 
   AspectRatio -> Automatic, 
   PlotStyle -> {{Darker@Cyan, Dashed}, {Darker@Cyan, 
      Dashed}, {Darker@Green, Dashed}, Darker@Green}, 
   Filling -> {3 -> {2}}, FillingStyle -> {None, LightRed}, 
   PlotRange -> {-1.5, 2.5}, AxesStyle -> Arrowheads[{0.05}], 
   GridLines -> {{{-2, {Thick, AbsoluteDashing[{3, 3}]}}}, None}, 
   Epilog -> {{AbsoluteThickness[1.75]}, AbsoluteDashing[3, 3], 
     Line[{{1 + 1/Sqrt[2], 0}, {1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}}], 
     Line[{{1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}, {0, 1 + 1/Sqrt[2]}}]}];
Show[f2, f1]

Answer 3

Graphics[{
  FaceForm[LightRed], EdgeForm[], 
  Disk[{1, 1}, 1, {Pi/4, Pi/4 - Pi}],
  AbsoluteThickness[1.75], Dashed, Black, 
  Line[{{1 + 1/Sqrt[2], 0}, {1 + 1/Sqrt[2], 1 + 1/Sqrt[2]}, {0, 1 + 1/Sqrt[2]}}],
  Darker @ Cyan, Circle[{1, 1}],
  Darker @ Green, InfiniteLine[{{0, 0}, {2, 2}}], 
  Dashing[{}], Line[{{0, 0}, {2, 2}}]}, 
 PlotRange -> {{-1.5, 2.5}, {-1.5, 2.5}},
 Axes -> True,
 AxesStyle -> Arrowheads[{0.05}]]

Answer 4

Here's a start:

RegionPlot[x^2 + y^2 < 1 \[And] y < x, {x, -1, 1}, {y, -1, 1},
 PlotStyle -> LightPink,
 PlotPoints -> 100,
 Epilog -> {Darker[Green], Thickness[0.01], Dashing[0.01], 
   Line[{{-1, -1}, {1, 1}}]}]