Multiple choice

Let $C_1, C_2$ be two circles touching each other externally at the point A and let AB be the diameter of circle $C_1$. Draw a secant $BA_3$ to circle $C_2$, intersecting circle $C_1$ at a point $A_1(\neq A)$, and circle $C_2$ at points $A_2$ and $A_3$. If $BA_1=2$, $BA_2=3$ and $BA_3=4$, then the radii of circles $C_1$ and $C_2$ are respectively.

  1. $\displaystyle\frac{\sqrt{30}}{5}, \frac{3\sqrt{30}}{10}$
  2. $\displaystyle\frac{\sqrt{5}}{2}, \frac{7\sqrt{5}}{10}$
  3. $\displaystyle\frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}$
  4. $\displaystyle\frac{\sqrt{10}}{3}, \frac{17\sqrt{10}}{30}$
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