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
A circle with radius 
is divided into twelve equal parts. The twelve dividing points are connected with the centre of the circle, producing twelve rays. Starting from one of the dividing points a segment is drawn perpendicular to the next ray in the clockwise sense; from the foot of this perpendicular another perpendicular segment is drawn to the next ray, and the process is continued ad infinitum. What is the limit of the sum of these segments (in terms of )?
is divided into twelve equal parts. The twelve dividing points are connected with the centre of the circle, producing twelve rays. Starting from one of the dividing points a segment is drawn perpendicular to the next ray in the clockwise sense; from the foot of this perpendicular another perpendicular segment is drawn to the next ray, and the process is continued ad infinitum. What is the limit of the sum of these segments (in terms of )?This post has been edited 1 time. Last edited by parmenides51, Dec 24, 2022, 6:21 PM
