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) MN is the diameter of the circle with centre O.
∠MOA + ∠AOB + ∠BON = 180°
⇒ 100° + ∠AOB + 35° = 180°
⇒ ∠AOB = 180° - 100° - 35° = 45°
Similarly, ∠COD = 45°
(2) Eqaual arcs subtend equal angles at the centre.
∠AOB = ∠COD = 45°
So, arc AB ≌ arc CD
(3) Corresponding chords of congruent arcs are congruent.
arc AB ≌ arc CD
So, chord AB ≌ chord CD