930 Some geometry problems from recent journals
American Mathematical Monthly, Problem 11006, proposed by B. Suceava, ̆
California State University, Fullerton, CA
LetABCbe an acute triangle,Tthe midpoint of arcBCof the circle
circumscribingABC. LetGandKbe the projections ofAandT re-
spectively onBC, letHandLbe the projections ofBandConAT,
and letEbe the midpoint ofAB. Prove that
(a) KH//AC,GL//BT,GH//T C, andLK//AB.(b)G,H,KandLare concyclic.(c) The center of the circle throughG,H, andK lies on the Euler
circle (nine-point circle) of triangleABC.