init_elements()
-- among the solutions, the center lying between the vertex and the contact point
local function inner_center(centers, v, t)
  local d = point.abs(t - v)
  for i = 1, centers:count() do
    local c = centers:get(i)
    if point.abs(c - v) < d then return c end
  end
end
local pos = ...
z.A = point(0,0)
z.B = point(10,0)
L.AB = line(z.A, z.B)
z.M = L.AB.mid
C.MB = circle(z.M, z.B)
z.X1 = point(8, 0)
L.X1X2 = L.AB:orthogonal_from(z.X1)
--z.P = intersection(L.X1X2, C.MB)
z.P =  C.MB:point(pos)
T.AMP = triangle(z.A, z.M, z.P)
L.MX3 = T.AMP:bisector(z.M)
z.C = intersection(L.MX3, C.MB)
T.PMB = triangle(z.P, z.M, z.B)
L.MX4 = T.PMB:bisector(z.M)
z.E = intersection(L.MX4, C.MB)
-- circle tangent to (MA) and (MP) through C, inside the sector
local centers = line(z.M, z.A):c_ll_p(line(z.M, z.P), z.C)
z.O1 = inner_center(centers, z.M, z.C)
local centers = line(z.M, z.B):c_ll_p(line(z.M, z.P), z.E)
z.O2 = inner_center(centers, z.M, z.E)