Q2 of 6 Page 118

In the adjoining figure O is the centre of the circle whose diameter is MN. Measures of some central angles are given in the figure. Hence, find the following


(1) m∠AOB and m∠COD


(2) Show that arc AB ≅ arc CD


(3) Show that chord AB ≅ chord CD


(1) In given figure, we can see that


∠NOC + ∠COD +∠DOM = 180° (linear pair)


35° +∠COD+100° =180°


∠COD = 180° - 135°= 45°


So ∠COD and ∠AOB = 45°


(2) arc AB ≅ arc CD because the arcs are of equal measure 45° each angle and equal angle made equal sector.


(3) chord AB ≅ chord CD because corresponding chords of congruent arcs are congruent.


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