[ Bisector of an angle (gMT).]

Find the geometric locus of points equidistant from two intersecting lines.
Consider the bisectors of the four angles formed by the given lines.

## Solution

Two intersecting lines divide the plane into four parts. If a point lies on the bisector of one of the four resulting angles, then it is equidistant from the given lines.

Conversely, any point in the plane, not lying on any of the given lines, is located inside one of the angles. If it is equidistant from the given lines, then it lies on the bisector of that angle. Clearly, the point of intersection of the given lines also satisfies the condition of the problem.

![](https://cdn.mathpix.com/cropped/2024_05_06_67482594d9a3488694ecg-26.jpg?height=349&width=761&top_left_y=1918&top_left_x=657)

## Answer

Two perpendicular lines