JAMB 1986 · UME · Q42

If $U$ and $V$ are two distinct fixed points and $W$ is a variable point such that $\angle UWV$ is a right angle, what is the locus of $W$ ?

Worked solution (try it first)

The angle in a semicircle is a right angle, and the converse holds too: if $\angle UWV = 90^\circ$ , then $W$ lies on the circle with $UV$ as diameter.
As $W$ moves round (on both sides of $UV$ ), it traces that whole circle.
So the locus is a circle with $UV$ as diameter, option D.