Maths Olympiad Exam

If x, y, z are the sides of a triangle, then prove that
|x^2(y - z) + y^2(z - x) + z^2(x - y)| < xyz.

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Maths Olympiad Other Question

In a triangle ABC, D is a point on BC such that AD is the internal bisector of A. Suppose
B = 2C and CD = AB. Prove that A = 72◦ Prove that the product of the first 200 positive even integers differs from the product of the
first 200 positive odd integers by a multiple of 401.