Question

in given fig OP bisect angle AOC, OP perpendicular to OQ,show that pointsA,O and B are collinear
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Answer 1

Step-by-step explanation:

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

frm[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}

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