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SMO 2011 Junior Round 1 Question 11

SMO · SMO 2011 Junior Round 1

Question 11

Suppose $\dfrac xa+\dfrac yb+\dfrac zc=\sqrt2$ and $\dfrac ax+\dfrac by+\dfrac cz=0$. Find $$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}.$$