MathDB
rhombus wanted, starting with an isosceles (Greece Junior 2003)

Source:

July 12, 2019
geometryrhombusisosceles

Problem Statement

Let ABCABC be an isosceles triangle (AB=ACAB=AC). The altitude AHAH and the perpendiculare bisector (e)(e) of side ABAB intersect at point MM . The perpendicular on line (e)(e) passing through MM intersects BCBC at point DD. If the circumscribed circle of the triangle BMDBMD intersects line (e)(e) at point SS , the prove that: a) BS//AMBS // AM . b) quadrilateral AMBSAMBS is rhombus.