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The quadrilateral formed by angle bisect...

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

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Given a quadrilateral `ABCD` with internal angle bisectors `AF`, `BH`, `CH` and `DF` of angles `A`, `B`, `C` and `D` respectively and the points `E`, `F`, `G` and `H` form a quadrilateral `EFGH`.
To prove that `EFGH` is a cyclic quadrilateral.
`/_HEF=/_AEB` (Vertically opposite angles)
Consider triangle `AEB`
`/_AEB+1/2/_A+1/2/_B=180`
`/_AEB=180-1/2/_A-1/2/_B`
...
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