# Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates. Download png

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Hey! I'm pretty sure that the answer is 38. You must connect the three points to make a triangle, then find the midpoint of each triangle, and make a line from each point through the door adjacent.

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You can find a point that is equidistant from all three points using algebra. But first, you should take a look at the geometry of the issue. If they are not located on the same line, you can say that there is a circle passing all of them and connecting them. A Circle is one of the easiest figures to deal with from the point of geometry as all its points are equidistant from the center.

The next step is to connect all these points into a triangle. Then, construct bisector of any two lines to find the center point.

When using algebra, you can build an equation, but it would be more complex than using the geometric median.