1995 IMO Problems/Problem 5
Problem
Let be a convex hexagon with
and
, such that
. Suppose
and
are points in the interior of the hexagon such that
. Prove that
.
Solution
Draw and
to make equilateral
and
, and draw points
and
such that
,
, directed angle
, and directed angle
to make equilateral
and
. Notice that
is on the circumcircle of
and
is on the circumcircle of
. By Ptolemy,
and
. So,
Notice that octagon
is symmetric about
. So,
. --tigerzhang