According to the journal of irreproducible results, any obtuse angle is a right angle! c d b p here is their argument. given the obtuse angle x, we make a quadrilateral abcd with \dab = x, and \abc = 90 , and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = p

d. so the triangles p ad and p bc have equal sides and are congruent. thus \pad = \pbc. but pab is isosceles, hence \pab = \pba. subtracting, gives x = \pad \pab = \pbc \pba = 90 . this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?