A Lemma(Problem?) I used for another problem.
by XmL, Aug 3, 2013, 7:12 PM
I used this lemma for the problem: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=47&t=547044
Here's the lemma:
In
. 
is the othocenter. 
is the result of a half turn of about the midpoint of 
. 
meets at 
. Let 
meet circle 
at a second point 
. Prove that 
bisects 
Proof:
Here's the lemma:
In
. 
is the othocenter. 
is the result of a half turn of about the midpoint of 
. 
meets at 
. Let 
meet circle 
at a second point 
. Prove that 
bisects 
Proof:
is the diameter of circle 
.
be the midpoint of 
is a point on 
.
are concyclic 
.
meet 
,
.
and 
,
.
and 
.
are concyclic, our desired result.This post has been edited 3 times. Last edited by XmL, Aug 12, 2014, 11:19 PM
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