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CHMMC problems
2012 CHMMC Spring
10
10
Part of
2012 CHMMC Spring
Problems
(1)
2012 Spring Team #10
Source:
3/20/2022
A convex polygon in the Cartesian plane has all of its vertices on integer coordinates. One of the sides of the polygon is
A
B
AB
A
B
where
A
=
(
0
,
0
)
A = (0, 0)
A
=
(
0
,
0
)
and
B
=
(
51
,
51
)
B = (51, 51)
B
=
(
51
,
51
)
, and the interior angles at
A
A
A
and
B
B
B
are both at most
45
45
45
degrees. Assuming no
180
180
180
degree angles, what is the maximum number of vertices this polygon can have?
combinatorics
geometry