A circle C_1 (center O_1, radius r_1=1 cm) is tangent to two sides of a square VWXY at a corner. Another circle C_2 (radius r_2) is tangent to the same two sides and also touches C_1. If the square side is 4 cm, find r_2 (in cm).

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ETAG General Aptitude QUESTION #3767

Question 1

A circle $C_1$ (center $O_1$, radius $r_1=1$ cm) is tangent to two sides of a square $VWXY$ at a corner. Another circle $C_2$ (radius $r_2$) is tangent to the same two sides and also touches $C_1$. If the square side is 4 cm, find $r_2$ (in cm).

4 - 3\sqrt{2}
1 + 2\sqrt{2}
7 - 4\sqrt{2}✔️
5 + 3\sqrt{2}

Correct Answer Explanation

Using the diagonal distance: $\sqrt{2}(3-r_2) = 1+r_2$. Solving gives $r_2 = 7-4\sqrt{2}$.

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