1958 AMC 12 Question 48 - thichhoctoan.com

Question 48

Diameter $\overline{AB}$ of a circle with center $O$ is $10$ units. $C$ is a point $4$ units from $A,$ and on $\overline{AB}.$ $D$ is a point $4$ units from $B,$ and on $\overline{AB}.$ $P$ is any point on the circle. Then the broken-line path from $C$ to $P$ to $D:$

has the same length for all positions of $P$
exceeds $10$ units for all positions of $P$
cannot exceed $10$ units
is shortest when $CPD$ is a right triangle
is longest when $P$ is equidistant from $C$
and $D$