r \; \frac{\sqrt{3}}{3}

r

|CG|=r \; (3-\frac{\sqrt{3}}{3})

|CH|=2r

M = Intersect(xAxis, yAxis)
r = 4 (slider from -5 to 10)
c = Circle(M, r)
A = Point(c)
f = Line(A, M)
d = Circle(A, M)
B_{1} = Intersect(c, d, 1)
g = OrthogonalLine(M, f)
C = Intersect(c, g, 1)
h = OrthogonalLine(C, g)
i = Ray(M, B_{1})
D = Intersect(h, i)
e = Circle(D, Segment[C, M])
E = Intersect(e, h, 1)
k = Circle(E, D)
F = Intersect(k, h, 2)
p = Circle(F, E)
G = Intersect(p, h, 2)
H = Intersect(c, g, 2)
j = Segment(H, G)
q = Circle(G, F)
I = Intersect(q, j, 1)
s = Semicircle(H, G)
l = OrthogonalLine(I, j)
J = Intersect(s, l, 1)
Quadrat, m, n, t_1, a, K, L = Polygon(J, G, 4)
F_K: (pi * r^(2))
Text1 = LaTeX(F_K, true, true)
Text2 = LaTeX(Quadrat, true, true)
N = Point(d)
O = Point(d)
c_1 = CircleArc(A, O, N)
b = Segment(H, C)
P = Point(h)
Q = Point(h)
f_1 = Segment(P, Q)
R = Point(i)
g_1 = Segment(M, R)
h_1 = Segment(M, A)
S = Point(l)
T = Point(l)
i_1 = Segment(S, T)
U = Point(q)
V = Point(q)
d_1 = CircleArc(G, U, V)
B = Intersect(c, g_1)
t = 11 (slider from 0 to 11, step 1)
W = (17.6542, 6.897552066115692)
Z = (17.6742, -6.082447933884292)

Tool: HöhenStrecke
Ein: Punkt von dem das Lot gefällt wird, zwei Punkte der Geraden, auf die das Lot gefällt wird   Aus: das Lot als Strecke
Input: C, A, B
Output: c

a = Line(A, B)
b = OrthogonalLine(C, a)
D = Intersect(a, b)
c = Segment(C, D)