Weber problem that, at the optimum, the angles between the AD, BD, and CD straight lines must be equal to 360° / 3 = 120°. Torricelli deduced from that conclusion that: 1– if any triangle ABD, whose ∠ADB angle is equal to 120°, generates an ABDE convex quadrilateral inscribed in a circle, the ∠ABE angle of the ABE triangle must be equal to (180° − 120°)= 60°; 2– one way to determine the set of locations of D for which the ∠ADB angle is equal to 120° is to draw an equilateral ABE triangle (because each angle of an equilateral triangle is
Reuleaux triangle one draws a third circle, again of the same radius, with its center at one of the two crossing points of the two previous circles, passing through both marked points. The central region in the resulting arrangement of three circles will be a Reuleaux triangle. Alternatively, a Reuleaux triangle may be constructed from an equilateral triangle "T" by drawing three arcs of circles, each centered at one vertex of "T" and connecting the other two vertices. Or, equivalently, it may be constructed as the intersection of three disks centered at the vertices of "T", with radius equal to the side