Can a rhombus that is NOT a square be inscribed in a circle? A quadrilaterals opposite angles must add up to 180 in order to be inscribed in a circle, but a rhombuses opposite angles are equal and do not add up to 180. Therefore, a rhombus that does not have 4 right angles cannot be inscribed in a circle. True or false?
$\endgroup$ 11 Answer
$\begingroup$a rhombus that is not a square cannot be inscribed in a circle. one reason is the one you gave that opposite angles of a cyclic quadrilateral must add up to $180^\circ$ and for a true rhombus this is not so.
another reason is that the center of the rhombus must coincide with the center of the circle by symmetry and the diagonals of the rhombus bisect each other at $90^\circ$ which will give you a square.
$\endgroup$
