## Problems to be Solved

**You may choose any three of the following problems. Your solutions must be typed and the documents placed in your Livebinder Portfolio.**

## Problem #1

Prerequisite knowledge:

- 3D coordinates and vectors
- scalar (dot) product of vectors

## Problem #2

It may be useful to construct this with a compass and a straightedge or using Geogebra and to draw auxiliary lines in your diagram. Prerequisite knowledge includes special triangles and area of sectors.

## Problem #3

An accurate construction may lead to some insight. Relatively prime means that two numbers have no common factors other than one. For example, 4 and 7 are relatively prime to one another even though 4 is not a prime number.

## Problem #4

This is a very challenging problem. It would help to think of this problem as a recursive sequence.