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2020 Stanford Mathematics Tournament
6
6
Part of
2020 Stanford Mathematics Tournament
Problems
(1)
SMT 2020 Geometry #6
Source:
8/9/2023
Consider triangle
A
B
C
ABC
A
BC
on the coordinate plane with
A
=
(
2
,
3
)
A = (2, 3)
A
=
(
2
,
3
)
and
C
=
(
96
13
,
207
13
)
C =\left( \frac{96}{13} , \frac{207}{13} \right)
C
=
(
13
96
,
13
207
)
. Let
B
B
B
be the point with the smallest possible
y
y
y
-coordinate such that
A
B
=
13
AB = 13
A
B
=
13
and
B
C
=
15
BC = 15
BC
=
15
. Compute the coordinates of the incenter of triangle
A
B
C
ABC
A
BC
.
geometry
analytic geometry