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1. 1. CIRCLES
2. 2. Circle is the collection of points in a plane that are all the same distance from a fixed point. The fixed point is called the center.
3. 3. The diameter starts at one side of the circle, goes through the center and ends on the other side. A line segment joining the center to any point on the circle is called radius.
4. 4. A line joining any pair of points on a circle, is called a chord of the circle. The longest chord DB, is called the diameter of the circle. AB,DB,CD are the chords of the circle
5. 5. The perpendicular from the center of a circle to a chord, passes through the midpoint of the chord.
6. 6. Prove that in a circle , chords of equal length are at equal distance from the center ? AE,BF are chords of equal length and OC, OD are perpendicular from the center O of the circle to these chords. We have ,AC = ½ AE and BD = ½ BF Since ,AE = BF. We get , AC = BD
7. 7. From the right angled triangle OAC, OBD , We get, OC2 = OA2 – AC2 OD2 = OB2 – BD2 Since, OA = OB (radius ) AC = BD , We get, OC2 = OD2 And so OC = OD