Y by
Let
be a triangle, and let
be the altitudes. Let
be a line passing through
. Suppose
intersect
at
, and
intersect
at
. Prove that:
i) If
is the
-median, then circles
and
are tangent.
ii) If
is the inner
-angle bisector, suppose
intersect
again at
, then
is perpendicular to
.










i) If




ii) If






