Olympiad workbookIOQMProperties of Triangles

a, b, c are positive real numbers such that a^2+b^2 =c^2 and a b=c . Determine the value of | (a+b+c)(a+b-c)(b+c-a)(c+a-b) c^2 | .

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aligned & a^2+b^2=c^2, a b=c & (a+b)^2=a^2+b^2+2 a b=c^2+2 c & (a+b)^2-c^2=2 c ...(i) & (a-b)^2=c^2-2 c c^2-(a-b)^2=2 c ...(ii) aligned Given expression is ((a+b)^2-c^2 ) (c^2-(a-b)^2 ) c^2 = 2 c 2 c c^2 =4

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