Two circles each of radius \( 5 \) units touch each other at the point \( (1, 2) \). If the equation of their common tangents is \( 4x + 3y = 10 \), and \( C_{1} (\alpha, \beta) \) and \( C_{2} (\gamma, \delta) \), \( C_{1} \ne C_{2} \) are their centres, then \( |(\alpha + \beta)(\gamma + \delta)| \) is equal to ________.
