Rectangle in SemiCircle

Drag point P to show different rectangles within the semicircle.  The areas and perimeters of these rectangle are plotted against the rectangle width in the 2nd-Graphics Window.

Move point C to alter the size of the semicircle.

Show Area Locus

Show Perimeter Locus

Area and Perimeter Values

A = Intersect(xAxis, yAxis)
C = Point(xAxis)
D = Midpoint(A, C)
prng = Segment(D, C)
c = Semicircle(A, C)
C_1 = Midpoint(A, C)
a = Segment(A, C)
P = Point(prng)
b = OrthogonalLine(P, a)
F = Intersect(c, b)
Q = Mirror(P, C_1)
d = OrthogonalLine(Q, a)
E = Intersect(c, d)
PolyArea, Height, f, e, Width = Polygon(P, F, E, Q)
PolyPer = Perimeter(PolyArea)
H: (Distance[P, Q], PolyPer)
G: (Distance[P, Q], PolyArea)
M = Max(y(G), y(H))
k = Line(G, H)
B = Intersect(k, xAxis)
LocA = Locus(G, P)
g = Segment(G, (x(G), 0))
h = false
RadiusSC: Distance[A, C] / 2
text1: "Radius = " + RadiusSC + "cm"
i = Segment(H, (x(H), 0))
LocP = Locus(H, P)
l = Segment((x(B), M), B)
j = false
m = true