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Let A, O, B be collinear with O ∈ (AB), C, O, D also collinear with...

Let A, O, B be collinear with O ∈ (AB), C, O, D also collinear with O ∈ (CD) E in the interior of the ∠AOC and F in the interior of the ∠BOD such that O ∈ (EF). If (OE is the bisector of the ∠AOC prove that (OF is the bisector of the ∠BOD

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Answer #1

Consider the picture. Suppose assume is the bisector of . Thus we have , say. Note that , thus . Again note that , thus , thus we have . Similarly by same argument shows that . Hence we have , hence bisects .

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