Coordinate Geometry: JEE Main 2021 Mathematics question

Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and C₁($\alpha$, $\beta$) and C₂($\gamma$, $\delta$), C₁ $\ne$ C₂ are their centres, then |($\alpha$ + $\beta$) ($\gamma$ + $\delta$)| is equal to ___________.