显示题目，并解答，和给出解题思路及分析过程---**Textual Information:** ∠ACB=90°, CA=6, AB=10, 点M是 BC上一动点, BD⊥AM, 设t=AM/DM 探究: t是否有最小值? **Mathematical Formulas/Equations:** ∠ACB=90° CA=6 AB=10 BD⊥AM t = AM / DM **Question Stem:** 探究: t是否有最小值? (Explore: Does t have a minimum value?) **Chart/Diagram Description:** * **Type:** Geometric diagram illustrating a triangle and related points and lines. * **Main Elements:** * A triangle ABC, with the right angle at vertex C. * Vertices are labeled A, B, and C. * Point M is a moving point located on the side BC. M is highlighted with a green circle. * Point D is the foot of the perpendicular from point B to the line containing segment AM. D is labeled. * A line segment CA is labeled with length 6. * A line segment AB is present, labeled with length 10 in the text. * Line segment AM is shown as a cyan line. * Line segment BD is shown as a pink line, connecting B to D. * A right angle symbol is shown at vertex C, indicating ∠ACB = 90°. * A right angle symbol is shown at point D, indicating that the line BD is perpendicular to the line AM (as stated in the text BD⊥AM and D is on AM). * Lines CB and AC form the sides of the right angle. * Line AB is the hypotenuse of triangle ABC.