In Year 2 we studied the circle as an object of Euclidean geometry: chords, central and inscribed angles, tangents, Euclid’s theorems on chords. In this chapter we look at it with fresh eyes, as a curve of the Cartesian plane. We shall learn to write its equation starting from centre and radius, to recognise when a second-degree equation really represents a circle, to study the relative positions of a line and a circle (external, tangent, secant) using the discriminant method or the distance method, to write the tangents drawn from a point, to intersect two circles by exploiting the radical axis, and finally to determine a circle starting from given geometric conditions.
Sections
- Equation of the circle
- Relative positions of line and circle
- Tangents from a point
- Intersection of two circles and radical axis
- Determining a circle