1975 AMC 12 Question 11
AMC12 · 1975 AMC 12
Let $P$ be an interior point of circle $K$ other than the center of $K.$ Form all chords of $K$ which pass through $P,$ and determine their midpoints. The locus of these midpoints is
a circle with one point deleted
a circle if the distance from $P$ to the center of $K$ is
less than one half the radius of $K;$ otherwise a circular arc of
less than $360^\circ$
a semicircle with one point deleted
a semicircle
a circle