Question

Given two squares with same centre and sides being parallel to the corresponding sides of the each other. If length of the side of the bigger square is X and the length of the smaller square is Y, find the length of the line joining AB.

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is A

Extend AB to C.
Draw OD perpendicular to the side of the bigger triangle as shown.
Given EC = X
The perpendicular from centre to the chord bisects it.
So $DC=\left(\frac{X}{2}\right)$
Using Pythagoras theorem on $\Delta ODC$ we get
$O{D}^2+D{C}^2=O{C}^{2}OC=\frac{x}{\sqrt{2}}$
Similarly in \Delta OHG we get,
$OG=\frac{Y}{\sqrt{2}}GC=OC-OG=\frac{(X-Y)}{\sqrt{2}}$