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Question
Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD=8m,BC=11m and AB=10m; then the distance (in meters) of a point M on AB from the point A such that MD2+MC2 is minimum is
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Solution
(MD)2+(MC)2=h2+64+(h−10)2+121
=2 h2−20 h+64+100+121
=2( h2−10 h)+285
=2( h−5)2+235
It is minimum if h=5
(MD)2+(MC)2=h2+64+(h−10)2+121
=2 h2−20 h+64+100+121
=2( h2−10 h)+285
=2( h−5)2+235
It is minimum if h=5
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