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2009年全国初中数学联赛第二试(A)的第三题是:已知a,b,c为正数,满足如下条件:a+b+c=32,(a+b-c)/(ab)+(b+c-a)/(bc)+(c+a-b)/(ca)=1/4证明以a~(1/2),b~(1/2),c~(1/2)为三边长可构成一个直角三角形.
The third question of the second trial (A) of the 2009 National Junior Middle School Maths League is that it is known that a, b and c are positive numbers and satisfy the following conditions: a + b + c = 32, (b + ca) / (bc) + (c + ab) / (ca) = 1/4 prove that a ~ (1/2), b ~ The three sides form a right-angled triangle.