Question 57
Given an equilateral triangle, find all points inside the triangle such that the distance from the point to one of the sides is equal to the geometric mean of the distances from the point to the other two sides of the triangle.
[The geometric mean of two numbers $x$ and $y$ equals $\sqrt{x y}$.]
[The geometric mean of two numbers $x$ and $y$ equals $\sqrt{x y}$.]