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Find the shortest distance from A to D given that one must at least touch the BC once

This is a open type question, better use some simple methods i wanna know more different kind of problem solving skills for this question, the more simple the methods the better

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    @Mathematics: Photons are tiny but their mathematical abilities should not be underestimated. They know that to minimize the path length, one should make the angle of incidence equal to the angle of reflection.2012-09-29

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Hint: Reflect $CD$ in line $BC$. Then $D$ goes to say $D'$. Draw $AD'$.

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    Because you asked for "without differentiation" in a comment, I assumed that the way you had done it was the standard calculus way.2012-09-29