Q. 143.8( 25 Votes )
Given, lines AB and CD intersect each other at point O.
OE is the bisector of ∠ BOD.
TO prove: OF bisects ∠AOC.
AB and CD intersect each other at point O.
Therefore, ∠ AOC = ∠ BOD
∠ 1 = ∠ 2 [OE is the bisector of ∠BOD] _________________ (i)
∠ 1 = ∠ 3 and ∠ 2 = ∠ 4 [Opposite angles] ____________ (ii)
From equations (i) and (ii)
∠ 3 = ∠ 4
Hence, OF is the bisector of ∠AOC.
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