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There is given convex quadrilateral ABCD. And internal bisectors of angle $<A$ and $<C$ intersect in point X. And internal bisectors of angle $<B$ and $<D$ intersect in point Y. And $<XAY = 90$ I'm struggling to do draw this construction , could anyone send me a photo of this construction?

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Here is an example, created with Cinderella using a bisection algorithm to adjust the angle.

Example construction

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Cross reference: the preceding comment was restated as a full question. I don't have a ready answer yet. –  MvG Dec 5 '12 at 13:25
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