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
Inscribed angle "V" and whose sides pass through points "A" and "B". Draw line "OA". Angle "BOA" is a central angle; call it "θ". Lines "OV" and "OA" are both radii of the circle, so they have equal lengths. Therefore, triangle "VOA" is isosceles, so angle "BVA" (the inscribed angle) and angle "VAO" are equal; let each of them be denoted as "ψ". Angles "BOA" and "AOV" are supplementary. They add up to 180°, since line "VB" passing through "O" is a straight line. Therefore, angle "AOV" measures 180° − "θ". It is known that the three angles of a triangle add