omg i haven't done geo in a month
by wu2481632, Nov 4, 2016, 3:08 PM
so rusty
Let
and 
be the circumcircle and the circumcentre of an acute-angled triangle 
with 
. The angle bisector of 
intersects at 
. Let 
be the circle with diameter 
. The angle bisectors of 
and 
intersect at points 
and 
respectively. The point 
is chosen on the line 
so that 
. Prove that 
. (ISL 2014 G3)
Let
and 
be the circumcircle and the circumcentre of an acute-angled triangle 
with 
. The angle bisector of 
intersects at 
. Let 
be the circle with diameter 
. The angle bisectors of 
and 
intersect at points 
and 
respectively. The point 
is chosen on the line 
so that 
. Prove that 
. (ISL 2014 G3)
and 
are simply the perpendicular bisectors of 
and 
.
and 
the second intersections of the perpendicular bisectors of 
is an isosceles trapezoid.
and lines 
.
.
.
the midpoint of 
.
is cyclic.
.
.
.
to this sum, which does indeed give us the full 
,
such that 
and 
.
,
.
is cyclic, and that 
is the radical axis of 
and 
.
is the radical axis of 
,
,
May 2017
April 2017