Question

plz help me friends... there are 50pts for you!

Answer 1

since
angle POC + angle QOC = 90°,

then

2× angle POC + 2× angle QOC =2×90°,

angle AOC + angle BOC =180°,

therefore AOB forms a linear pair then A, O and B are collinear

Answer 2

Hey mate!

∠AOP = ∠COP [Since OP bisects ∠AOC] ...(i)
∠BOQ = ∠COQ [Since OQ bisects ∠BOC] ...(ii)
Now,
∠AOB = ∠AOP + ∠POC + ∠COQ + ∠QOB
=> ∠POC + ∠POC + ∠COQ + ∠COQ [From (i) and (ii)]
=> 2(∠POC + ∠COQ)
=> 2(∠POQ)
=> 2(90°)
=> 180°
Therefore, by converse of Linear Pair Axiom,
points A, O and B are collinear.

Hope it helps :)