# Monthly Archives: January 2017

## Three Intersecting Circles

Circle has a radius of and its center is at . Circle has a radius of and its center at . What is the length of the radius of a third circle (Circle ) that passes through the center of … Continue reading

## Complicated Quadratic Root

What is the (simplified) value for which the larger root of is ? Source: NCTM Mathematics Teacher, October 2006 Solution We are going to take advantage of the formulas and repeatedly in the process of simplifying the complicated root. First, we multiply the … Continue reading

## How Many Liars?

Winkin said, “We’re all liars.” Blinkin replied, “Only you are a liar.” Finkin said, “You’re both liars.” If each of them always tells the truth or always lies, how many of the three are liars? Source: NCTM Mathematics Teacher, October … Continue reading

## Triples of Real Numbers

What are all ordered triples of real numbers that satisfy ? Source: NCTM Mathematics Teacher, October 2006 Solution Add the three equations Substitute the value of into the equations Solve for yields . Substitute the value of into the equations Solve … Continue reading

## Trains Passing Each Other

At noon, a train leaves New York for Toronto while another leaves Toronto for New York. It takes one train hours and the other hours to make the trip. If both maintain constant speeds and travel along parallel tracks, at … Continue reading

## Largest of Five Integers

A set contains five integers. When distinct elements of this set are added together, two at a time, the complete list of different possible sums is , and . What is the largest of the five integers in the set? … Continue reading