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2023 UMD Math Competition Part I
#17
Three medians
Three medians
Source: UMD 2023 I #17
October 22, 2023
UMD
geometry
Problem Statement
The lengths of the sides of triangle
A
′
B
′
C
′
A'B'C'
A
′
B
′
C
′
are equal to the lengths of the three medians of triangle
A
B
C
.
ABC.
A
BC
.
Then the ratio
A
r
e
a
(
A
′
B
′
C
′
)
/
A
r
e
a
(
A
B
C
)
\mathrm{Area} (A'B'C') / \mathrm{Area} (ABC)
Area
(
A
′
B
′
C
′
)
/
Area
(
A
BC
)
equals
a
.
1
2
b
.
2
3
c
.
3
4
d
.
5
6
e
.
Cannot be determined from the information given.
\mathrm a. ~ \frac 12\qquad \mathrm b.~\frac 23\qquad \mathrm c. ~\frac34 \qquad \mathrm d. ~\frac56 \qquad \mathrm e. ~\text{Cannot be determined from the information given.}
a
.
2
1
b
.
3
2
c
.
4
3
d
.
6
5
e
.
Cannot be determined from the information given.
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