SOLUTION: Let AB be a chord in a circle centered at O with radius r. For what point M on the arc AB the sum of the distances [AM]+[MB] is minimum. Find this distance in terms of the radius r

Question 192580: Let AB be a chord in a circle centered at O with radius r. For what point M on the arc AB the sum of the distances [AM]+[MB] is minimum. Find this distance in terms of the radius r and the distance d=[AB].
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I really wonder whether you really meant to say "the sum of the distances AM + BM is a minimum," because what you have formed is a triangle with sides

. The Triangle Inequality tells us that AM + BM must always be greater than AB, unless, of course, M is coincident with either A or B such that you no longer have a triangle and AM + BM = 0 + d = d or AM + BM = d + 0 = d -- such being the minimum limiting case.

John

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