Question

Two coins are kept in a square of side 1 as shown in the diagram. The sum of the radii of coins is

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is C

Suppose the coins have radii R and r.
The centres of the coins and the point where they touch divide the diagonal into four line segments with lengths R$\sqrt{2}$ , R, r, r$\sqrt{2}$.
Since the diagonal has length $\sqrt{2}$, it follows that (R + r) ($\sqrt{2}$ + 1) = $\sqrt{2}$,
So R + r = $\frac{\sqrt{2}}{\sqrt{2}+1}$ = (2 - $\sqrt{2}$)