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The x-coordinate of the incentre of the...

The x-coordinate of the incentre of the triangle where the midpoints of the sides are (0, 1) (1, 1) and (1, 0) is

A

`2+sqrt(2)`

B

`2-sqrt(2)`

C

`1+sqrt(2)`

D

`1-sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B


Let vertex A be (a, b).
R is mid point of AB.
`therefore B " is " (-a, -b+2)`
Pis mid point of BC.
`therefore C " is " (a+2, -2+b)`
Q is mid point of AC.
`therefore a=0 " and " b=2`
`therefore " Abscissa of in center"`
`I_(x)=(0 xx 2+0 xx sqrt(8) +2 xx 2)/(2+2+2sqrt(2))`
`therefore I_(x)=(4)/(4+2sqrt(2))`
`rArr I_(x)=(2)/(2+sqrt(2)) xx (2-sqrt(2))/(2-sqrt(2))`
`rArr I_(x)=(2(2-sqrt(2)))/(2) = 2-sqrt(2)`
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