document.write( "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]. \n" ); document.write( "
Algebra.Com's Answer #144573 by solver91311(24713)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "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.\r
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