Please solve q 94 ?

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1 Answer
CW
May 21, 2018

#CF=2# units

Explanation:

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By tangent-secant theorem, we know :
#ED^2=EB(EB+BA)#
#=> ED^2=8(8+4)=96, => ED=4sqrt6#
As #DeltaEDA# is right angled at #D#,
#=> AD^2=AE^2-ED^2=12^2-96=48#,
#=> AD=sqrt48=4sqrt3#
Now, as #AD# is the diameter, #=> angleACD=90^@#,
#=> DC^2=AD^2-AC^2=48-6^2=12#,
#=> DC=sqrt12=2sqrt3#
let #CF=x#,
as #DeltaDFC and DeltaADC# are similar,
#=> (CF)/(CD)=(CD)/(CA)#
#=> (CF)/sqrt12=sqrt12/6#
#=> CF=12/6=2# units

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