yes; yes; no; no; Because all[br]points on a circle are the same[br]distance from the center,[br][math]\overline{AB}≅\overline{AE}≅\overline{AC}≅\overline{AD}[/math]. So,[br]the diagonals of quadrilateral[br]BDCE bisect each other, which[br]means it is a parallelogram by[br]the Parallelogram Diagonals[br]Converse (Thm. 7.10). Because[br]all 4 angles of BDCE are right[br]angles, it is a rectangle. BDCE is[br]neither a rhombus nor a square[br]because [math]\overline{BD}[/math] and [math]\overline{EC}[/math] are not[br]necessarily the same length as[br][math]\overline{BE}[/math] and [math]\overline{DC}[/math].

The quadrilateral formed by the[br]endpoints of two diameters is a[br]rectangle (and a parallelogram).[br]In other words, a quadrilateral[br]is a rectangle if and only if its[br]diagonals are congruent and[br]bisect each other.