Please solve q 121 ?

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Answer 1 · 2018-05-29T11:22:40

#color(blue)(1/(sqrt(2)+1)#

Answer (4)

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#OC=1# radius of larger circle.

#/_AOB=90^@# coordinate axes.

#OC# bisects #/_AOB=>/_COD=45^@#

For #Delta OCD#

#sin(45)=(CD)/(OC)=>CD=OCsin(45)=sin(45)#

#Delta OPB# ~ #Delta OCD# similar triangles.

Similarity property:

#(OP)/(OC)=(PB)/(CD)#

#OP=OC-PC=1-PC#

Using

#(OP)/(OC)=(PB)/(CD)#

#:.#

#(1-PB)/1=(PB)/(sin(45)#

#sin(45)=sqrt(2)/2#

#(1-PB)/1=(PB)/(sqrt(2)/2)#

#1-PB=(2sqrt(2)PB)/2#

#2=2sqrt(2)PB+2PB#

#PB=2/(2sqrt(2)+2)=1/(sqrt(2)+1)#

Since PB is the radius of the smaller circle:

#r=1/(sqrt(2)+1)#