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Perpendicular Medians

Problem

In triangle $ABC$, $A'$ is the midpoint of $BC$, $B'$ is the midpoint of $AC$, and the line segments $AA'$ and $BB'$ are perpendicular. Let $AC = b$, $BC = a$, and $AB = c$.

  1. Find $c$ in terms of $a$ and $b$.
  2. Determine the values of $b$ in terms of $a$ for which the triangle exists.
  3. Calculate the size of the maximum interior angle at vertex $C$.
Problem ID: 296 (10 Dec 2006)     Difficulty: 4 Star

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