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
Exterior angle theorem segments). Only one of these angles contains the third side of the triangle in its interior, and this angle is called an "interior angle" of the triangle. In the picture below, the angles "∠ABC", "∠BCA" and "∠CAB" are the three interior angles of the triangle. An "exterior angle" is formed by extending one of the sides of the triangle; the angle between the extended side and the other side is the exterior angle. In the picture, angle "∠ACD" is an exterior angle. The proof of Proposition 1.16 given by Euclid is often cited as one place where Euclid gives a