Nachos

By Reid Valentine

Problem

Alberto, Juan, and Steve are hungry for some nachos, and not just any kind of nachos, they're looking for those gross ones made from cheese food that just taste so good! The only problem is that somehow, they know that the nachos are at an equal distance from each of them and now they must triangulate the nachos! They remembered from high school geometry that they now need to find the circumcenter so that they can eat those delicious nachos!

Construction

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Construction Steps

1-Bisect the sides by making two x marks above and below the segment, putting the tip of the compass on the point and placing the pencil a little over half the line and make an arc. Repeat above and below the segment from both points.

2-Draw a line through the two x marks. This will bisect the line perpendicularly.

3- Repeat this for each segment. The point where the new lines intersect is the circumcenter. This point is an equal distance from all three of the points or people.

Calculations

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Explanation

I chose to use circumcenter because I knew that all tree of the people (points) were the same distance from the nachos and a circumcenter find the POC where all points are an equadistance from the point. The distance from the POC to the vertexes are radii of the circumcircle which is the smallest perfect circle that touches all of the three points on the triangle. To find this POC you must use perpendicular bisectors on all three of the sides and they will all intersect at one point.