Question

in the given figure, OP bisects angleAOC, OQ bisects angleBOC and OP perpendicular to OQ. show that points A,O and B are collinear.

Answer 1

Since OP is the bisector of ∠AOC 
∴∠AOP=∠COP                                          [1]

Since OQ is the bisector of ∠BOC
∴∠BOQ=∠COQ                                          [2]

Now consider ∠AOB
=∠AOP+∠COP+∠COQ+∠BOQ
=∠COP+∠COP+∠COQ+∠COQ

from[1] and [2]
=2[∠CoP+∠COQ]
=2∠POQ
=2(90°) 

∴OP⊥OQ=180°
thus we can say that A,O and B lies on the same line   {linear pair}

Hope it is helpful

please mark me the brainleist and follow me