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Girls in Math at Yale
2021 Girls in Math at Yale
R6
R6
Part of
2021 Girls in Math at Yale
Problems
(1)
GiM at Yale 2021 Mathathon R6: oops no flavortext
Source:
2/28/2021
16. Suppose trapezoid
J
A
N
E
JANE
J
A
NE
is inscribed in a circle of radius
25
25
25
such that the center of the circle lies inside the trapezoid. If the two bases of
J
A
N
E
JANE
J
A
NE
have side lengths
14
14
14
and
30
30
30
and the average of the lengths of the two legs is
m
\sqrt{m}
m
, what is
m
m
m
?17. What is the radius of the circle tangent to the
x
x
x
-axis, the line
y
=
3
x
y=\sqrt{3}x
y
=
3
x
, and the circle
(
x
−
10
3
)
2
+
(
y
−
10
)
2
=
25
(x-10\sqrt{3})^2+(y-10)^2=25
(
x
−
10
3
)
2
+
(
y
−
10
)
2
=
25
? 18. Find the smallest positive integer
n
n
n
such that
3
n
3
−
9
n
2
+
5
n
−
15
3n^3-9n^2+5n-15
3
n
3
−
9
n
2
+
5
n
−
15
is divisible by
121
121
121
but not
2
2
2
.
Yale
college