Quadrilateral identity

In a convex quadrilateral , Bisectors of ABC and BAD meet at . Show that .
Sadly, no ideas on this one.

Quote:

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Originally Posted by atreyyu

In a convex quadrilateral , Bisectors of ABC and BAD meet at . Show that .
Sadly, no ideas on this one.

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1. I assume that you mean the angle bisector ... ? (Drawn in blue) If so:

2. Draw a sketch (see attachment)

3. For symmetry reasons the 2 orange segments must be as long as the red segment.