Please ask the math master to answer my question in detail. Why is DN+Mn the smallest when N moves to the intersection of bm and ac?

Connect BN, because AD=AB=8, AN=AN, Angle DAN= Angle BAN=45 degrees.

So triangle BAN= triangle DAN, so BN=DN.

Then DN+MN=BN+MN makes DN+MN the smallest and BN+MN the smallest.

According to the principle of shortest straight line, B, N and M are on the same straight line, BN+MN=BM, and N is on the AC line, so N is the intersection of BM and AC. Because the angle MCB=90 degrees, BC=8, MC=DC-DM=8-2=6,

According to Pythagorean Theorem, BM 2 = 8 2+6 2 = 100, BM = 10 (negative values are discarded), that is, the minimum value of DN+MN is10.

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