def napoleonic(A: Scene.Point, B: Scene.Point, C: Scene.Point):
c0 = A.circle_through(B)
c1 = B.circle_through(A)
line = A.line_through(B, layer='auxiliary')
V = c0.intersection_point(c1, label=C.label + '1')
equilateral = Scene.Triangle(A, B, V)
V.opposite_side_constraint(C, line)
scene.centroid_point(equilateral, label=C.label + '2')
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
triangle2 = Scene.Triangle(
*[side.middle_point() for side in triangle.sides])
D = scene.circumcentre_point(triangle, label='D')
E = scene.orthocentre_point(triangle2, label='E')
return scene
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
A.segment(B).perpendicular_constraint(A.segment(C))
I = scene.incentre_point(triangle, label='I')
J = scene.orthocentre_point(Scene.Triangle(A, B, I), label='J')
return scene
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
A.segment(B).perpendicular_constraint(A.segment(C))
I = scene.incentre_point(triangle, label='I')
J = scene.orthocentre_point(Scene.Triangle(A, B, I), label='J')
# Additional constructions
D = A.line_through(B).intersection_point(I.line_through(J), label='D')
E = A.line_through(I).intersection_point(B.line_through(J), label='E')
return scene
def napoleonic(A, B, C):
circleAB = A.circle_through(B, layer='invisible')
circleBA = B.circle_through(A, layer='invisible')
V = circleAB.intersection_point(circleBA, label=C.label + '_1')
equilateral = Scene.Triangle(A, B, V)
A.scene.equilateral_constraint(equilateral,
comment=LazyComment(
'Given: %s is equilateral',
equilateral))
line = A.line_through(B, layer='auxiliary')
V.opposite_side_constraint(C,
line,
comment=LazyComment(
'Given: %s is outward of %s', V, triangle))
D = scene.circumcentre_point(equilateral, label=C.label + '_2')
from sandbox import Scene
from sandbox.property import ProportionalLengthsProperty
from sandbox.util import LazyComment
from visualiser import visualise
scene = Scene()
A, D, C, B = scene.square('A', 'D', 'C', 'B')
A.x = 0
A.y = 0
D.x = 1
D.y = 0
I = scene.incentre_point(Scene.Triangle(A, B, C), label='I')
side = A.line_through(C)
foot = scene.perpendicular_foot_point(I, side, layer='auxiliary')
I.circle_through(foot)
prop = ProportionalLengthsProperty(B.segment(C), D.segment(I), 1)
visualise(
scene,
prop,
title='Onestep Problem 1',
task=[
LazyComment('%s is a square', Scene.Polygon(A, B, C, D)),
LazyComment('%s is the incentre of %s', I, Scene.Triangle(A, B, C)),
LazyComment('Prove, that |%s| = |%s|', D.segment(I), B.segment(C))
],
reference=
'Problem 1 from <a href="http://www.stanleyrabinowitz.com/download/onestepresults.pdf">onestep results list</a> by <a href="https://www.facebook.com/stanley.rabinowitz">Stanley Rabinowitz</a>'
from runner import run_sample
from sandbox import Scene
from sandbox.property import ProportionalLengthsProperty
scene = Scene()
A, B, C, D = scene.square('A', 'B', 'C', 'D', non_degenerate=True)
I = scene.incentre_point(Scene.Triangle(A, B, C), label='I')
prop = ProportionalLengthsProperty(B.segment(C), D.segment(I), 1)
run_sample(scene, prop)