Circles important notes intermediate students
In this chapter we are going to learn the difinition of a ‘circle’ and discuss about its general equation, its tangents and normals and various other properties like the power of a point, pole and polar with respect to a circle. Relative positions of two Circlces and thier common tangents.
The locus of a point in a plane which moves in such a way that its distance from a fixed point in the plane is always a constant, is called a circle.
RADII AND CHORD
We begin by recapitulating the definition of a circle and the terminology used for circles. Throughout this module, all geometry is assumed to be within a fixed plane.
- A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the centre).
- Any interval joining a point on the circle to the centre is called a radius. By the definition of a circle, any two radii have the same length. Notice that the word ‘radius’ is being used to refer both to these intervals and to the common length of these intervals.
- An interval joining two points on the circle is called a chord.
- A chord that passes through the centre is called a diameter. Since a diameter consists of two radii joined at their endpoints, every diameter has length equal to twice the radius.
- The word ‘diameter’ is use to refer both to these intervals and to their common length.
- A line that cuts a circle at two distinct points is called a secant. Thus a chord is the interval that the circle cuts off a secant, and a diameter is the interval cut off by a secant passing through the centre of a ‘circle’.