## Wheel Rolling Inside Wheel A wheel of radius 10 inches rolls inside a wheel of radius 54 inches. Point P1 on the little rolling wheel starts at point P on the fixed wheel. After how many revolutions of the little wheel do points P and P1 coincide once more?

## Trapezoid, Similar Triangles Let ABCD be a trapezoid with the measure of base AB twice that of base DC, and let E be the point of intersection of the diagonals. If the measure of diagonal AC is 11, then what is the measure of segment EC?

1. 11/3
2. 15/4
3. 4
4. 7/2
5. 3

## Spinning in Circles

We humans are traveling around in circles without even knowing it. We travel a circle around the axis of the earth once a day, and an almost-circle around the sun once a year. Considering each trip independently, how fast do we travel in each circle? (Assume we’re on the equator.) Here are some helpful data:

• The diameter of the Earth is 12,756 km at the equator;
• The distance from the Earth to the sun is 149,600,000 km;
• There are 365.26 days in a year.
• Give each answer in kilometers per hour.

## Find Diameter of Circle

AB is a diameter of a circle. Tangents AD and BC are drawn so that segments AC and BD intersect at a point E on the circle. If AD = a and BC = b, with ab, then the diameter AB is: a. |ab|
b.
 a + b 2
c. ab
d.
 ab a + b
e.
 ab 2(a + b)

## Stack of Water Pipes Three of the new water pipes for Main Street are stacked as shown. The external diameter of each pipe is 12 inches. How tall is the stack (h in the picture)?

## Gertrude Goldfish

Two young men in tuxedos are walking down the street at about 10 pm. One of them is carrying a round goldfish bowl filled with water. There is a goldfish, named Gertrude, in the bowl. As they pass a round pool in the park, the goldfish gets very excited and jumps out of the bowl into the pool, right at the edge. She starts swimming due north. She hits the wall after she has swum exactly 30 feet. She heads east, and, after going 40 feet, she hits the wall again. Once she regains consciousness after this second collision, she calculates the diameter of the pool. What is it? And what is the story about the two guys in their tuxes?

## Tetrahedron in Cube Four of the 8 vertices of a cube are vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron.

1. 2
2. 3
3. 2
4. 3
5. 2