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ALL FAS ame Gircle SS = SS ae โโโ _โ Learning Objectives At the course of this chapter, you will be able to: 13-1. aes tangents and tangent line of a 13-3, Obtain normal of circle circle 13-2, Learn the parametric and diametric form of circle Definition THEOREM 2 A circle is the locus of a point which moves in a plane in (@)_ The perpendicular from the centre of circle to a chord such a way that its distance from a fixed point remains bisects the chord. constant. The fixed point is called the centre of the circle Converse and the constant distance is called the radius of the circle, Basic Theorems and Results of Circles 1. Concentric circles: Circles having same centre. 2, Congruent circles: Iff their radii are equal. 3. Congruent arcs: Iff they have same degree measure at the centre. THEOREM 1 (a) If evo arcs of a circle (or of congruent circles) are congruent, the corresponding chords are equal. Converse , : If two chords of a circle are equal then their corresponding arcs are congruent. (b) Equal chords of a circle (or of congruent circles) sub- tend equal angles at the centre. Converse . If the angle subtended by two chords of a circle (or of congruent circle) at the centre are equal, the chords are equal. The line joining the mid-point of a chord to the centre of a circle is perpendicular to the chord. (b) Perpendicular bisectors of two chords of a circle inter- sect at its centre. THEOREM 3 (a) There is one and only one circle passing through three non collinear points. (b) If two circles intersects in two points, then the line joining the centres is perpendicular bisector of com- mon chords. THEOREM 4 (a) Equal chords of a circle (or of congruent circles) are equidistant from the centre, Converse 5 Chords of a circle (or of congruent circles) which are equi- distant from the centre are equal. (b) Iftwo equal chords are drawn from a point on the circle, then the centre of circle will lie on angle bisector of these two chords. โ A (c) Of any two chords of a circle larger will be near to centre, 
