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In a triangle ABC if angle ABC=60^(@), t...

In a triangle ABC if `angle ABC=60^(@)`, then `((AB-BC+CA)/(r ))^(2)=`

A

10

B

11

C

12

D

14

Text Solution

Verified by Experts

The correct Answer is:
C
`r=(s-a)tan((A)/(2))`
`therefore r=((AB+BC+CA)/(2)-BC)(1)/(sqrt(3))`
`tehrefore r=(1)/(sqrt(3))(AB-BC+CA)/(2)`
`therefore 2sqrt(3)=(AB-BC+CA)/(r )`
`therefore ((AB-BC+CA)/(r ))^(2)=12`
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