In the figure above, the circles are centered at \(O(0, 0)\) and \(P(10, 0).\) Line \(AB\) is tangent to both circles,

[Vincen]

In the figure above, the circles are centered at \(O(0, 0)\) and \(P(10, 0).\) Line \(AB\) is tangent to both circles, at points \(A\) and \(B\) respectively, and intersects the \(x\)-axis at point \(X.\) What is the \(x\)-coordinate of point \(X ?\)

(1) The area of the circle centered at point \(P\) is \(4\) times the area of the circle centered at point \(O.\)

(2) \(BX\) is twice as long as \(AX.\)

Answer: D

Source: Manhattan GMAT