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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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well, actually, i have solved this question but i wanna know more problem solving techniques to this question – Mathematics Sep 29 '12 at 4:45
Better with some easy method without using any differentiation – Mathematics Sep 29 '12 at 4:46
If you have solved the problem then maybe you should edit your solution into the question so we don't waste our time telling you things you already know. – Gerry Myerson Sep 29 '12 at 5:45
@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. – André Nicolas Sep 29 '12 at 21:01

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

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Yup, this is what i use to solve this question, but can you solve with with different methods? – Mathematics Sep 29 '12 at 7:06
Because you asked for "without differentiation" in a comment, I assumed that the way you had done it was the standard calculus way. – André Nicolas Sep 29 '12 at 14:57

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