Parallelogram Parallelogram In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The
Ex-tangential quadrilateral distance between the circumcenter and the excenter, then where "R" and "r" are the circumradius and exradius respectively. This is the same equation as Fuss's theorem for a bicentric quadrilateral. But when solving for "x", we must choose the other root of the quadratic equation for the ex-bicentric quadrilateral compared to the bicentric. Hence, for the ex-bicentric we have From this formula it follows that which means that the circumcircle and excircle can never intersect each other. Ex-tangential quadrilateral In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the "extensions" of all four sides are tangent to a