The circle is the figure richest in properties in plane geometry. In this chapter we study all the objects that live around the circle and the theorems that relate them: arcs and chords, the measure of angles in radians, the link between central angle and inscribed angle, the tangents from an external point, the angle between tangent and chord, and the intersecting chords theorem. From here we move on to the notable points of the triangle — centroid, orthocentre, incentre and circumcentre — and to the inscribed and circumscribed circles, closing with a few notable triangles and some applications of analytic geometry (point–line distance and the perpendicular bisector of a segment).
Sections
- Arcs, chords and radians
- Central and inscribed angles
- Tangents from an external point
- Angle between tangent and chord
- Radius of the circumscribed circle
- Radius of the inscribed circle
- Angle bisector theorem
- Arithmetic mean and geometric mean
- Intersecting chords theorem
- Notable points of the triangle
- 30°-60°-90° right triangle
- 45°-45°-90° isosceles right triangle
- Distance of a point from a line
- Perpendicular bisector of a segment in coordinates