WOLFRAM|DEMONSTRATIONS PROJECT

Reflections of a Line through the Orthocenter in the Sides of an Acute Triangle

​
labels
altitudes
reflections
circumcircle
A line
l
is drawn through the orthocenter
H
(the intersection point of the altitudes) of an acute-angled triangle. Prove that the symmetric images
l
a
,
l
b
,
l
c
of
l
with respect to the sides
BC
,
CA
,
AB
have a point in common, which lies on the circumcircle of
ABC
.