and 
,
cookies from one of the piles, of which he eats 
and puts 
for which Marica has a winning strategy.
be non-negative real numbers such that 
Prove that
Y by Adventure10
On the extension of chord 
of a circle centroid at 
a point 
is taken and tangents 
and 
to the circle are drawn from it with 
and 
lying on the circle, let 
be the midpoint of the line segment 
. If 
then determine with proof the magnitude of 
.
of a circle centroid at 
a point 
is taken and tangents 
and 
to the circle are drawn from it with 
and 
lying on the circle, let 
be the midpoint of the line segment 
. If 
then determine with proof the magnitude of 
.
an
X
.
and 
are similar.Therefore 
= 
,
.
.
= 
implying 
are concyclic. Therefore 
= 180− 
= 
.
=180− 
.
