where 
and 
intersect at two points 
and 
.
be the line tangent to these circles at 
and 
,
be the line parallel to 
on 
on 
and 
meet at 
;
and 
;
and 
.
.
be a scalene triangle such that 
is its incircle. 
is tangent to 
.
)
.
,
,
be the incircles of the triangles 
,
,
,
is inscribed in a circle 
where 
,
is the intersection of diagonals 
and 
,
bisects the angle 
prove that 
Y by
The evil sorceress Morgana lives in a square-shaped palace divided into a 
grid of rooms, each initially at a temperature of 
C. Merlin attempts to freeze Morgana by casting a spell that permanently sets the central cell's temperature to 
C.
At each subsequent nanosecond, the following steps occur in order:
1. For every cell except the central one, the new temperature is computed as the arithmetic mean of the temperatures of its adjacent cells (those sharing a side).
2. All new temperatures (except the central cell) are updated simultaneously to the calculated values.
Morgana can freely move between rooms but will freeze if all room temperatures drop below
degrees. The ice spell lasts for 
nanoseconds, after which temperatures revert to their initial values.
Will Merlin succeed in freezing Morgana?
grid of rooms, each initially at a temperature of 
C. Merlin attempts to freeze Morgana by casting a spell that permanently sets the central cell's temperature to 
C.At each subsequent nanosecond, the following steps occur in order:
1. For every cell except the central one, the new temperature is computed as the arithmetic mean of the temperatures of its adjacent cells (those sharing a side).
2. All new temperatures (except the central cell) are updated simultaneously to the calculated values.
Morgana can freely move between rooms but will freeze if all room temperatures drop below
degrees. The ice spell lasts for 
nanoseconds, after which temperatures revert to their initial values.Will Merlin succeed in freezing Morgana?
