$s_0=|BC|$
$h_0=|BH|$. Note $h_0=s_0/2$.
$s_1=|BD|$.
1. Use the Pythagorant theorem to find 
an equation relating $|BG|$ and $s_1$?
2. Express the area of $\triangle ABC$ as a function of $s_0$
3. Express the area of $\triangle ABC$ as a function of $
s_1$ and $s_0$.
4. Use 2. and 3 to find an equation relating $s_0$ and $s_1$. 

A = Intersect(xAxis, yAxis)
B = (1, 0)
c = Circle(A, B)
C = Point(c)
a = LineBisector(C, B)
D = Intersect(c, a, 2)
E = Tool2(A, B, D)
F = Tool2(A, B, E)
G = Intersect(c, a, 1)
b = Segment(B, G)
s_1 = Segment(D, B)
s_0 = Segment(B, C)
poly1, g, d_1, b_1 = Polygon(D, B, G)
H = Intersect(a, s_0)
h_0 = Segment(B, H)
d = Segment(C, A)
I = Point(xAxis)
poly2, i, c_1, a_1 = Polygon(C, A, I)

Tool: Half Arc (command HalfArc)
Marc point c
Input: xAxis, yAxis, B, C
Output: D

A = Intersect(xAxis, yAxis)
c = Circle(A, B)
a = LineBisector(C, B)
D = Intersect(c, a, 2)

Tool: Tool2
Center of circle, two points in teh circle
Input: A, B, C
Output: D

c = Circle(A, B)
a = LineBisector(C, B)
D = Intersect(c, a, 2)