Circles C1, C2, and C3, with centers O1, O2, and O3, and radii r1, r2, and r3,…

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Circles C1, C2, and C3, with centers O1, O2, and O3, and radii r1, r2, and r3, respectively, touch each other as shown in the following figure. Given r1 = 2 cm, r2 = 1 cm and the angle ∠O1O3O2 is 90°, r3 = _____ cm.

1. A.

   $\frac{1}{2}(-3 + \sqrt{17})$

2. B.

   $\frac{1}{2}(3 + \sqrt{17})$

3. C.

   $\frac{1}{2}(-2 + \sqrt{17})$

4. D.

   $\frac{1}{2}(-3 + 2\sqrt{17})$

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