Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 2004. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 31)

SASHALMI, É. and HOFFMANN, M., Generalizations of Bottema's theorem on pedal points

Generalizations of Bot tenia's theorem on pedal points 31 Figure 4. Finally we remark, that the orientation of the builded rectangles in Theorem 7 is important only in terms of homothety. If the rectangles are builded in a way that always their longer sides coincide to the segments defined by the pedals, then the sum of the areas of the "left" rectangles remains equal to the "right" one, but the large rectangle is no longer similar to the original one: the ratio of its sides is A'B

' _ a

2 + b

2 B'C ~ 2

ab ' where a and b are the sides of the original rectangle. References [1] BOTTEMA, O., De Elementaire Meetkunde van het Platte Vlak

, Nordhoff, 1938. [2] DERGIADES, N., VAN LAMOEN, F., Rectangles attached to sides of a triangle, Forum Geom. 3 (2003), 145 159. [2] EHRMANN, J. P., VAN LAMOEN, F., Some similarities associated with pedals, Forum Geom. 2 (2002), 163-166. [3] KIM BURLING, C., Triangle centers and central triangles, Congressus Numerantinum 129 (1998), 1-285. Éva Sashalmi and Miklós Hoffmann Department of Mathematics Károly Eszterházy College Leányka sir. 4. H-3300 Eger, Hungary E-mail: saske@ektf.hu; hofi@ektf.hu