MathDB

16. Suppose trapezoid

JANE

is inscribed in a circle of radius

25

such that the center of the circle lies inside the trapezoid. If the two bases of

JANE

have side lengths

14

and

30

and the average of the lengths of the two legs is

\sqrt{m}

, what is

m

?
17. What is the radius of the circle tangent to the

x

-axis, the line

y=\sqrt{3}x

, and the circle

(x-10\sqrt{3})^2+(y-10)^2=25

?
18. Find the smallest positive integer

n

such that

3n^3-9n^2+5n-15

is divisible by

121

but not

2

Problem Statement