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BMT Problems
2017 BMT Spring
19
19
Part of
2017 BMT Spring
Problems
(1)
center of ellipse through midpoints of triangle 2017 BMT Individual 19
Source:
1/3/2022
Let
T
T
T
be the triangle in the
x
y
xy
x
y
-plane with vertices
(
0
,
0
)
(0, 0)
(
0
,
0
)
,
(
3
,
0
)
(3, 0)
(
3
,
0
)
, and
(
0
,
3
2
)
\left(0, \frac32\right)
(
0
,
2
3
)
. Let
E
E
E
be the ellipse inscribed in
T
T
T
which meets each side of
T
T
T
at its midpoint. Find the distance from the center of
E
E
E
to
(
0
,
0
)
(0, 0)
(
0
,
0
)
.
conics
ellipse
geometry
analytic geometry