Question

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

Answer 1

(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) Equal 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