Harmonic quadrilateral

In Euclidean geometry, a harmonic quadrilateral, or harmonic quadrangle, is a quadrilateral that can be inscribed in a circle (cyclic quadrilateral) in which the products of the lengths of opposite sides are equal. It has several important properties.

Properties
Let $ABCD$ be a harmonic quadrilateral and $M$ the midpoint of diagonal $AC$. Then:
 * Tangents to the circumscribed circle at points $A$ and $C$ and the straight line $BD$ either intersect at one point or are mutually parallel.
 * Angles $∠BMC$ and $∠DMC$ are equal.
 * The bisectors of the angles at $B$ and $D$ intersect on the diagonal $AC$.
 * A diagonal $BD$ of the quadrilateral is a symmedian of the angles at $B$ and $D$ in the triangles ∆$ABC$ and ∆$ADC$.
 * The point of intersection of the diagonals is located towards the sides of the quadrilateral to proportional distances to the length of these sides.