Kadir Altintas - perpendicularity problem

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sunken rock
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Kadir Altintas - perpendicularity problem

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In quadrilateral $ABCD: \angle ABD=69^\circ, \angle ADB=37^\circ, \angle CBD=23^\circ, \angle BDC=7^\circ$.
Prove that $AC\perp BD$.

Note: the problem admits (at least) a fully synthetical solution, looking for other nice ideas.

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sunken rock
A blind man sees the details better.
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