Prove that 
be real numbers such that 
Prove that 
Where 
be a triangle with circumcircle 
.
and 
respectively denote the midpoints of the arcs 
and 
that do not contain the third vertex. Let 
denote the midpoint of arc 
(the arc 
including 
)
be the incenter of 
be the circle that is tangent to 
be the circle that is tangent to 
,
friends, 
people are seated around a circular table in a fixed order. Ali places 
Y by Adventure10, Mango247
A circle is circumscribed around the triangle 
. 
, 
, 
respectively the midpoints of 
. The sides 
, and 
intersect pairs of segments 
, 
and 
in pairs of points 
, 
and 
respectively. Prove that 
if and only if the triangle is equilateral.
. 
, 
, 
respectively the midpoints of 
. The sides 
, and 
intersect pairs of segments 
, 
and 
in pairs of points 
, 
and 
respectively. Prove that 
if and only if the triangle is equilateral.This post has been edited 1 time. Last edited by parmenides51, Sep 9, 2020, 6:51 AM
