3. In an equilateral $\triangle ABC$, $P$ is a point on side $AB$, $Q$ is a point on side $AC$, and $AP = CQ$. It is measured that the distance between point $A$ and the midpoint $M$ of line segment $PQ$ is $19 \mathrm{~cm}$. Then the distance from point $P$ to point $C$ is $\qquad$ $\mathrm{cm}$.
3. 38 .