# 10 tangents, 20 feets!

Geometry Level pending

Let $$P_i$$ and $$P'_i$$ be the feet of perpendiculars drawn from foci $$S$$ and $$S'$$ on a tangent $$T_i$$ to the ellipse $$E: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$$ whose length of major axis is 40 units.

If $$\ \displaystyle \sum_{i=1}^{10} (SP_i)(SP'_i) = 2560$$, then find the value of $$100e$$.

Details:

'$$e$$' denotes the eccentricity of the ellipse.

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