Russian Math Olympiad Problems: And Solutions Pdf Verified

In this paper, we have presented a selection of problems from the Russian Math Olympiad, along with their solutions. These problems demonstrate the challenging and elegant nature of the competition, and we hope that they will inspire readers to explore mathematics further.

In a triangle $ABC$, let $M$ be the midpoint of $BC$, and let $I$ be the incenter. Suppose that $\angle BIM = 90^{\circ}$. Find $\angle BAC$.

Let $x, y, z$ be positive real numbers such that $x + y + z = 1$. Prove that $\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \geq 1$.

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russian math olympiad problems and solutions pdf verified
russian math olympiad problems and solutions pdf verified
russian math olympiad problems and solutions pdf verified
russian math olympiad problems and solutions pdf verified
russian math olympiad problems and solutions pdf verified
russian math olympiad problems and solutions pdf verified
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