Given the circle c(O,R) (with center O and radius R), one diameter AB and midpoint C of the arc AB. Consider circle c1(K,KO), where center K lies on the segment OA, and consider the tangents CD,CO from the point C to circle c1(K,KO). Line KD intersects circle c(O,R) at points E and Z (point E lies on the semicircle that lies also point C). Lines EC and CZ intersects AB at points N and M respectively. Prove that quadrilateral EMZN is an isosceles trapezoid, inscribed in a circle whose center lie on circle c(O,R). geometrytrapezoidisosceles