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The incentre of a triangle with vertices...

The incentre of a triangle with vertices `(7, 1),(-1, 5)` and `(3+2sqrt(3),3+4sqrt(3))` is

A

`(3+(2)/(sqrt(3)),3+(4)/(sqrt(3)))`

B

`(1+(2)/(3sqrt(3)),1+(4)/(3sqrt(3)))`

C

`(7,1)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A

`:' AB = BC = CA =4sqrt(5)`
i.e., given triangle is equilateral.
Hence, incentre `= ((7-1+3+2sqrt(3))/(3),(1+5+3+4sqrt(3))/(3))` (centroid) `=(3+(2)/(sqrt(3)),3+(4)/(sqrt(3)))`
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