Q In the given figure OP bisects $\angle AOC .OQ bisects \angle BOC and OP\perp OQ$.Show that the points A,O,B  are collinear.

 

Dear Student,

Here is the solution of your asked query:

given: OP bisects ∠AOC and OQ bisects ∠BOC.

TPT: AOB are collinear points.

proof:

OP bisects ∠ AOC ⇒ ∠AOP = ∠ POC = 1/2 ∠AOC

OQ bisects ∠BOC ⇒ ∠BOQ = ∠ COQ = 1/2 ∠BOC

again , given that

∠ POC + ∠COQ = 90 deg

therefore

∠ AOB = 180 deg

thus AOB is a straight line and A, O and B are collinear points.