Muhammad's Congruent circles

Geometry Level 3

Two congruent circles \( \Gamma_1 \) and \( \Gamma_2 \) each have radius \( 213, \) and the center of \( \Gamma_1 \) lies on \( \Gamma_2.\) Suppose \( \Gamma_1 \) and \( \Gamma_2 \) intersect at \( A \) and \( B \). The line through \( A \) perpendicular to \( AB \) meets \( \Gamma_1 \) and \( \Gamma_2 \) again at \(C\) and \(D\), respectively. Find the length of \(CD\).

This problem is posed by Muhammad A.

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