be a cyclic quadrilateral. Let 
,
be the feet of the perpendiculars from 
to the lines 
,
,
if and only if the bisectors of 
and 
are concurrent with 
.
be reals such that 
. Prove that
be the feet of the altitudes from 
and 
as the reflections of 
be the circumcircle of 
.
with 
with 
is the circumcenter of 
can be inscribed within a circle.
Y by Adventure10
Points 
and 
are inner for 
for an acute 
, where is between 
and . Let 
, and 
be the feet of the perpendiculars from to 
, from 
to 
, and from 
to , respectively. Point 
is the middle point of . If 
and 
, prove that points 
, and 
lie on one circle, if and only if the lines 
, and 
intersect in one point.
and 
are inner for 
for an acute 
, where is between 
and . Let 
, and 
be the feet of the perpendiculars from to 
, from 
to 
, and from 
to , respectively. Point 
is the middle point of . If 
and 
, prove that points 
, and 
lie on one circle, if and only if the lines 
, and 
intersect in one point.This post has been edited 1 time. Last edited by Pinko, Sep 19, 2019, 8:06 AM
