a
Prove that
on one side and a 
on the other. Harry has 
of these coins arranged in a line from left to right. He repeatedly performs the following operation: if there are exactly 
coins showing 
t
the process starting with the configuration 
would be 
,
,
be the number of operations before Harry stops. For example, 
and 
.
possible initial configurations 
,
,
of the
,
,
, 
.
such that
Y by
Let 
be an acute triangle, and let 
be a point inside the triangle . Let 
be the midpoint of the segment ![$[PC]$](//latex.artofproblemsolving.com/7/8/1/7818452d29e34a743729cef6d6762490b71f626d.png)
, 
the intersection point of lines 
and 
, and 
the intersection point of lines 
and 
. Show that, if the angles 
and 
are equal, then 
.
be an acute triangle, and let 
be a point inside the triangle . Let 
be the midpoint of the segment ![$[PC]$](http://latex.artofproblemsolving.com/7/8/1/7818452d29e34a743729cef6d6762490b71f626d.png)
, 
the intersection point of lines 
and 
, and 
the intersection point of lines 
and 
. Show that, if the angles 
and 
are equal, then 
.This post has been edited 1 time. Last edited by parmenides51, Jun 21, 2022, 2:01 AM
