Question -
Answer -
Given : AB and CD intersect each other at O. OE is the bisector of тИаAOD and EO is produced to F.
┬а
To prove : OF is the bisector of тИаBOC
Proof : тИ╡ AB and CD intersect each other at O
тИ┤ тИаAOD = тИаBOC (Vertically opposite angles)
тИ╡OE is the bisector of тИаAOD
тИ┤ тИа1 = тИа2
тИ╡ AB and EF intersect each other at O
тИ┤тИа1 = тИа4 (Vertically opposite angles) Similarly, CD and EF intersect each other at O
тИ┤ тИа2 = тИа3
But тИа1 = тИа2
тИ┤ тИа3 = тИа4
OF is the bisector of тИаBOC