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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.