Question

Please solve q 94 ?

Answer 1

`CF=2` units

Explanation:

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