## A Problem with Parabolas

Let $P$ be the parabola with equation $y=x^2$ and let $Q$ be a parabola with a horizontal axis of symmetry. Suppose that $P$ and $Q$ intersect at $(1,1)$, $(3,9)$, and at one other point. Find the equation of the axis… Continue Reading

Astute geometry students know that when a problem involves a 3 and a 4, the answer will involve a 5 and the solution will make use of a right triangle somehow. The triple of numbers $(3,4,5)$ is called a Pythagorean… Continue Reading

## Three Circles in a Triangle: A Problem

This week, I was playing around with some geometry and came up with a fun problem. Suppose there is a triangle, $\Delta ABC$. Inside the triangle are three circles, each of which is tangent to the other circles and to… Continue Reading

## Maximizing the Product: A Problem

This week I offer a problem: What is the largest possible product you can make with a group of positive integers if the sum of those integers is 2017? Here we do not assume that the integers are distinct from… Continue Reading

## Binary Patterns: A Puzzle

Imagine a world in which there are only 2 digits. We are used to having 10 digits, from 0 to 9, but with just 2 of them, we’d be limited to 0 and 1. We could count in that world… Continue Reading

## A Question on Ellipses, Part 1

It is well known that the tangent lines to a circle are those lines that intersect the circle only once. The normal lines are perpendicular to the tangent lines at the point of tangency. All normal lines of a circle pass through… Continue Reading