Two straight lines intersect at a point O. A point moves so that its perpendicular distances from the two lines are always equal. Which statement about its path is TRUE?

The set of points equidistant from two intersecting lines is the pair of angle bisectors at O. If one pair of vertically opposite angles measures θ, its bisector makes θ/2 with a line while the bisector of the adjacent angle makes (180° − θ)/2 on the other side; the two bisectors therefore differ by θ/2 + (180° − θ)/2 = 90°, so they are perpendicular.