# If the opposite sides of a cyclic quadrilateral are extended to meet, say at points E and F, then the internal angle bisectors of the angles formed at points E and F are perpendicular.

Given ABCD is a cyclic quadrilateral .AB and DC are produced to meet at E whereas AD and BC are produced to meet at F.
Internal angle bisectors of $\angle E$  and $\angle F$  meet at O.

To prove $\angle EOF=90°$

Construction :- Extend FO to meet AB at N .

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