Capítulo 11 · Neste capítulo você vai
Angles on the circumference
- measure arcs by central angle;
- prove that the inscribed angle measures half the arc;
- recognize quadrilaterals inscriptible;
- calculate segment angles and eccentric angles.
Arched bridges, domes, maps, and even the knobs on touch screens use the properties of arcs and angles in the circumference. Eudoxus of Cnidus (4th century BC) studied in depth the proportions between arches; Euclid brought together in The Elements the central theorem of this chapter — the inscribed angle is worth half the arc —; and, in the 12th century, the Persian Omar Khayyam solved cubic equations crossing parabolas and circles.
