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The solution relies on using the sine rule.

Suppose that the perimeter of triangle ABC is P.

Then you need to divide P into 3 parts in the ratio of sin(A) : sin(B) : sin(C).

Let sin(A) + sin(B) + sin(C) = X. Then

AB = P*sin(C)/X

BC = P*sin(A)/X

CA = P*sin(B)/X

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