Question

A spirit shop outside the hockey stadium sells merchandise representing the three school districts that built the arena. The entrances to the arena, the spirit shop, and the parking lot form the vertices Of a triangle. The planning committee has decided to erect a memorial statue and would like it to be equidistant from the entrances to the arena, spirit shop, and the parking lot. At what point should the statue be located? Explain your answer.

Answer 1

The statue should be located at point E. Point E is the center of the circumscribed circle of the triangle created by the entrances to the arena, the spirit shop, and the parking lot. The distance from the statue to each vertex will then be equal to the radius of the circumscribed circle, so the statue will be at the same distance from all three landmarks.