Q.

Asked by Shambhu Nath Pandey | 25th Dec, 2015, 09:13: PM

Expert Answer:

Refer to the figure below:
 
J o i n i n g space t h e space f o u r space c e n t r e s space o f space t h e space c i r c l e s comma w e space g e t space a space s q u a r e space o f space s i d e space 2 r. H e n c e comma space d i a g o n a l space A C equals 2 square root of 2 r A C equals A E plus E F plus C F rightwards double arrow 2 square root of 2 r equals r plus E F plus r rightwards double arrow E F equals open parentheses 2 square root of 2 minus 2 close parentheses r E F space i s space t h e space d i a m e t e r space o f space t h e space i n n e r space c i r c l e. H e n c e comma space r a d i u s space o f space t h e space i n n e r space c i r c l e space i s space fraction numerator open parentheses 2 square root of 2 minus 2 close parentheses r over denominator 2 end fraction equals open parentheses square root of 2 minus 1 close parentheses r

Answered by satyajit samal | 27th Dec, 2015, 07:03: AM