Prove that the midpoints of the sides of a quadrilateral lie on a . . . Let us prove that if a quadrilateral is not orthodiagonal, then the midpoints of the quadrilateral are not concyclic Let me use the figure you drew Let $\angle{AOD}=\alpha$ where $\alpha\not=90^\circ$ Since $\angle{PYD}=\alpha$ and $\angle{AXP}=\alpha$, we have $$\angle{XPY}=360^\circ-\angle{PYO}-\angle{PXO}-\angle{XOY}=\alpha $$
Orthodiagonal quadrilateral - Mathematics Stack Exchange Is it always possible to construct an orthodiagonal quadrilateral such that the diagonals and perimeter are fixed? More specifically, given 2 fixed diagonals, how is the perimeter of the quadrilate
$a^2 + b^2 +c^2 +d^2 = 8r^2$ for orthodiagonal quadrilateral Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Please help me finish this proof - Mathematics Stack Exchange Prove that the midpoints of the sides of a quadrilateral lie on a circle if and only if the quadrilateral is orthodiagonal 5 Proving $(A\times B)^- = A^-\times B^-$ (closure of cartesian product)
geometry - ABCD is a cyclic quadrilateral whose two diagonals are . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Prove that the diagonals of a rhombus are orthogonal. I'm trying to solve some of the problems in Ahlfors' Complex Analysis book On the section about analytic geometry, the following problem is stated: Prove that the diagonals of a rhombus are ortho