As shown in the figure, circle C1 with center O1 and radius r1 touches the…

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As shown in the figure, circle C1 with center O1 and radius r1 touches the square VWXY at points P and Q while circle C2 with center O2 and radius r2 touches the square VWXY at points R and S. The two circles touch each other at T.

Given r1 = 1 cm and $\overline{VY} = \overline{VW} = 4\text{ cm}$, r2 = _____ cm.

1. A.

   $4 - 3\sqrt{2}$

2. B.

   $1 + 2\sqrt{2}$

3. C.

   $7 - 4\sqrt{2}$

4. D.

   $5 + 3\sqrt{2}$

Attempted by 10 students.