Literally Too Many Variables!

Algebra Level 2

p2a2+q2b2+r2c2 \large \dfrac{p^2}{a^2}+\dfrac{q^2}{b^2}+\dfrac{r^2}{c^2}

If pa+qb+rc=1\dfrac{p}{a}+\dfrac{q}{b}+\dfrac{r}{c}=1 and ap+bq+cr=0\dfrac{a}{p}+\dfrac{b}{q}+\dfrac{c}{r}=0, then compute the expression above.

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