Question

OP bisects _AOC , OQ bisects _BOC and OP is perpendicular to OQ. show that A, O and B are collinear points.

Answer 1

OP bisect angle AOC
∠AOP = ∠POC  so  ∠COP= 1/2 ∠COA

OQ bisects angle BOC
∠COQ = ∠QOB
∠COQ=1/2 ∠BOC

∠POQ = ∠COP + ∠COQ = 90 degree

then by subsituiting
1/2 ∠COA + 1/2 ∠BOC = 90 degree
1/2 (∠COA + ∠BOC) = 90
∠AOC + ∠COB = 180 
They form a linear pair do they are collinear 

Answer 2

OP bisect angle AOC

∠AOP = ∠POC  so  ∠COP= 1/2 ∠COA

OQ bisects angle BOC

∠COQ = ∠QOB

∠COQ=1/2 ∠BOC

∠POQ = ∠COP + ∠COQ = 90 degree

then by subsituiting

1/2 ∠COA + 1/2 ∠BOC = 90 degree

1/2 (∠COA + ∠BOC) = 90

∠AOC + ∠COB = 180 

They form a linear pair do they are collinear 

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