Slični zadaci
Let be an acute-angled triangle. The lines , and are constructed through the vertices , and respectively according the following prescription: Let be the foot of the altitude drawn from the vertex to the side ; let be the circle with diameter ; let meet the sides and at and respectively, where and are distinct from ; then let be the line through perpendicular to . The lines and are constructed similarly. Prove that the lines , and are concurrent.
Let be a convex quadrilateral whose vertices do not lie on a circle. Let be a quadrangle such that are the centers of the circumcircles of triangles , and . We write . Let us define
(a) Prove that and are similar.
(b) The ratio of similitude depends on the size of the angles of . Determine this ratio.
(a) Prove that and are similar.
(b) The ratio of similitude depends on the size of the angles of . Determine this ratio.