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Objectives

The students will be able to
  • define the terms related to circle
  • prove the following theorems and their converses:

(i) Equal chords of a circle subtend equal angles at the centre

(ii) The perpendicular from the centre to a chord bisects the chord

(iii) There is one and only one circle passing through three non-collinear points

(iv) Equal chords of a circle are equidistant from the centre

(v) Congruent arcs of a circles subtend equal angles at the centre

(vi) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle

(vii) Angles in the same segment of a circle are equal

(viii) Angle in a semicircle is a right angle

(ix) The sum of either pair of opposite angles of a cyclic quadrilateral is 180°


 




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