be an acute-angled triangle with 
and let 
be the foot of the
-
.
and 
in line 
and 
respectively. A line through 
and 
respectively such that 
while 
and 
and 
are tangent to each other.
with circumcircle 
.
in 
is the angle bisector of 
.
intersects 
.
be the midpoint of arc 
angle bisector of 
if and only if 
.
be real numbers satisfying
.
Y by Adventure10, Mango247
A convex quadrilateral intersects a circle at points 
and 
. (Note that for some letter 
, points 
and 
are on one side of the quadrilateral. Also, the points lie in that specific order on the circle.) Prove that if 
, then quadrilateral formed by these four segments is cyclic.
and 
. (Note that for some letter 
, points 
and 
are on one side of the quadrilateral. Also, the points lie in that specific order on the circle.) Prove that if 
, then quadrilateral formed by these four segments is cyclic.
,
,
,
(the four intersections which are internal to the original circle) - but then concluded that what we are supposed to prove is not generally true.
then the quadrilateral formed by the segments 
is cyclic.
and so forth such that the points on the quadrilateral are 
in order.
Similarly, 
Then it suffices to show that 
Because arcs subtended by chords of the same length have equal measure, we find that 
and 
Then it suffices to show that 
but this is clearly true because 
