a) Find the locus of the points that are equidistant from two parallel lines.
b) Find the locus of the points that are equidistant from two intersecting lines.
Find the locus of the midpoints of the segments, the ends of which are found on two given parallel lines.
The triangle \(ABC\) is given. Find the locus of the point \(X\) satisfying the inequalities \(AX \leq CX \leq BX\).
Find the locus of the points \(X\) such that the tangents drawn from \(X\) to a given circle have a given length.
The point \(A\) is fixed on a circle. Find the locus of the point \(X\) which divides the chords that end at point \(A\) in a \(1:2\) ratio, starting from the point \(A\).