91Ó°ÊÓ

Given distinct points \(A\) and \(B,\) all points equidistant from \(A\) and \(B\) and no others lie on the perpendicular bisector to \([A B]\).

Suppose that \(\triangle A B C\) has right angle at \(C\). Show that for any \(X \in[A C]\) the distance from \(X\) to \((A B)\) is smaller than \(A B\).

A line and a circle can have at most two points of intersection.

Make a ruler-and-compass construction of a line thru a given point that is perpendicular to a given line.