给老谢画的图(平面几何中的动点与最值问题)

如图, (ABot BD), (ACot CD), (AB=AC=sqrt{2}), (BD=CD=1), (P)为线段(AB)的中点, (M)为线段(AD)上的动点, 求(PM+dfrac{sqrt{2}}{2} MC)的最小值.