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In a !ABC , AB = 2, BC =4 ,CA = 3. If D ...

In a `!ABC , AB = 2, BC =4 ,CA = 3`. If D is the mid-point of BC, then the correct statement(s) is/are

A

`cosBne11/16`

B

`cosCne7/8`

C

`ADne2.4`

D

`AD^(2)=2.5`

Text Solution

Verified by Experts

We have,
`cosB=(AB^(2)+BC^(2)-AC^(2))/(2AB.BC)=(4+16-9)/(2xx2xx4)=11/16`

In `DeltaABD`, we have
`AD^(2)=AB^(2)+BD^(2)-2AB.BDcosB`
`rArrAD^(2)=2^(2)+2^(2)-2xx2xx2xx11/16=2.5`
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