Two Perpendicular Chords

Geometry Level 4

In circle \( \Gamma\), two chords \(AB, CD\) are perpendicular at \(E\). We have \(AE = 3 , EB = 7 , EC = 1 \). Let the radius of \(\Gamma\) be \(R\). What is the value of \(R^2\)?

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