The figure below shows a point D
inside an isosceles triangle ABC (AB = BC) so that
angle DCB = 2 angle BAD and DC = BC. BD extended meets AC at G,
CD extended meets AB at H, and the bisector of angle ABC meets
AD extended at N. Prove that (1) GN is perpendicular to BC at M;
(2) ABNG is concyclic at O_{1}; (3) ACNH is concyclic at O_{2}; (4)
CGDN is concyclic at O_{3}; (5) BCGH is concyclic at O_{4}; (6)
O_{1}NO_{4}O_{3}O_{2} is concyclic at G; (7) G is the circumcenter of
triangle ADH. This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.
See
also:
Geometry art of problem 1163
