Question

(Theoretical) If from O a point in AB two straight lines OC, OD are drawn onopposite sides of AB so as to make the angle COB equal to the angleAOD; show that OC and OD are in the same straight line.​

Answer 1

In circle with centre O and ∠AOC = 150°

But ∠AOC + reflex ∠AOC = 360°

∴ 150° + reflex ∠AOC = 360°

⇒ Reflex ∠AOC = 360° – 150° = 210°

Now arc AEC subtends ∠AOC at the centre and ∠ABC at the remaining part of the circle.



Reflex ∠AOC = 2∠ABC

⇒ 210° = 2∠ABC

∴ ∠ABC = 210∘2  = 105°