Reuleaux general triangle. Construction.
[EN] This construction makes a shape of constant width d. You can move A, B, C and d.
[FR] Cette construction donne une forme de Reuleaux de largeur constante d à partir d'un triangle quelconque ABC.
Questions.
1)
[EN] Write the three equations expressing d in terms of a, b, c, x, y, z.
[FR] Exprimer d de trois manières en fonction de a, b, c, x, y, z.
2)
[EN] Prove that x+y+z=(3d-a-b-c)/2.
[FR] Prouver que: x+y+z=(3d-a-b-c)/2.
3)
[EN] Set s:=(3d-a-b-c)/2. Prove that:
[FR] On pose s:=(3d-a-b-c)/2. Prouver que:
x=a+s-d, y=b+s-d, z=c+s-d.