1966 AMC 12 Question 32
AMC12 · 1966 AMC 12
Let $M$ be the midpoint of side $AB$ of triangle $ABC.$ Let $P$ be a point on $AB$ between $A$ and $M,$ and let $MD$ be drawn parallel to $PC$ and intersecting $BC$ at $D.$ If the ratio of the area of triangle $BPD$ to that of triangle $ABC$ is denoted by $r,$ then:
$\dfrac12\lt r\lt1$ depending upon the position of $P$
$r=\dfrac12$ independent of the position of
$P$
$\dfrac12\leq r\lt1$ depending upon the position of
$P$
$\dfrac13\lt r\lt\dfrac23$ depending upon the position of
$P$
$r=\dfrac13$ independent of the position of $P$