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GATE BT 2026 | GA | Question: 10

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As shown in the figure, circle $C_{1}$ with center $O_{1}$ and radius $r_{1}$ touches the square $V W X Y$ at points $P$ and $Q$ while circle $C_{2}$ with center $O_{2}$ and radius $r_{2}$ touches the square $V W X Y$ at points $R$ and $S$. The two circles touch each other at $T$.

Given $r_{1}=1 \mathrm{~cm}$ and $\overline{V Y}=\overline{V W}=4 \mathrm{~cm}, r_{2}=$ $\_\_\_\_$ cm.

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

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