/*  given 3 line-lengths, construct a triangle  */
/*  Calculate triangle apex with intersecting circles  */

hyp_s : 5$
long_s : 4$
short_s : 3$
load('newton1)$
kill(t)$  /*  remove value; symbol used by newton()  */
  /*  Discover one angle of triangle by Newton's method  */
t : newton(cos(t)*long_s+sin(t)*short_s-hyp_s, t, .7, 1E-6)$
k : [[0, 0], [hyp_s, 0], [cos(t)*long_s, sin(t)*long_s], [0, 0]]$
kill(t)$  /*  remove value; for [parametric]  */

plot2d([ [discrete, k],
  [parametric, cos(t)*long_s, sin(t)*long_s, [t, 0, 2*%pi]],
  [parametric, cos(t)*short_s+hyp_s, sin(t)*short_s, [t, 0, 2*%pi]]
  ], [legend, "triangle", concat("r = ", long_s), concat("r = ", short_s)],
  [color, green, red, blue], [y, -1 - long_s, 1 + long_s], same_xy);


hyp_s : 5$
long_s : 4$
short_s : 3$
  /* Discover angle by dividing into 2 right triangles, then trigonometry  */
answ : linsolve([
  long_s / hyp_s - x / long_s,  /*  cosine; x, unknown 'long'  */
  short_s / hyp_s - height / long_s,  /*  sine; height, unknown 'short'  */
  short_s / long_s - height / x  /*  tangent; long_s, known hypotenuse   */
  ],
[x, height])$
k : [[0, 0], [hyp_s, 0], [subst(answ[1], x), subst(answ[2], height)], [0, 0]]$

draw2d (yrange=[-1 - long_s, 1 + long_s],
  proportional_axes='xy, points_joined=true, point_type=none,
  color=green, key="triangle", points(k), nticks=300,
  color=red, key=concat(" r = ", long_s),
  parametric(cos(t)*long_s, sin(t)*long_s, t, 0, 2*%pi),
  color=blue, key=concat(" r = ", short_s),
  parametric(cos(t)*short_s+hyp_s, sin(t)*short_s, t, 0, 2*%pi) );