In ` A B C ,a=5,b=12 ,c=90^0a n dD` is a point on `A B` so that `/_B C D=45^0dot` Then which of the following is not true? `C D=(60sqrt(2))/(17)` (b) `B D=(65)/(17)` `A D=(60sqrt(2))/(17)` (d) none of these

Options

A. `CD = (60 sqrt2)/(17)`
B. `BD = (65)/(17)`
C. `AD = (60 sqrt2)/(17)`
D. none of these

Answer

C

Explanation

In `Delta CDB, (C)/(sinB) = (BC)/(sin (135^(@) - B))`
`rArr CD = (BC sin B)/(sin (135^(@) - B))`
`= (5sqrt2)/(1 + cot B) = (5 sqrt2)/(1 + (5)/(12))`

`:. CD = (60 sqrt2)/(17)`
Also from triangle, `(CD)/(sin B) = (BD)/(sin 45^(@))`
`rArr BD = (65)/(17)`
`rArr AD = 13 - (65)/(17) = (156)/(17)`