Question

The x-coordiante of the incentre of the triangle that has the coordiantes of mid points of its sides as (0,1),(1,1) and (1,0) is:
A. `2+sqrt(2)`
B. `2-sqrt(2)`
C. `1+sqrt(2)`
D. `1-sqrt(2)`

Answer 1

Given mid-points of a triangle are `(0,1)`, `(1,1)` and `(1,0)`. Plotting these points on a graph paper and make a triangle.
So, the sides of triangle will be `2,2` and `sqrt(2^(2)+2^(2))` i.e. `2sqrt(2)`.

`x`-coordinate of incentre `=(2xx0+2sqrt(2)*0+2*2)/(2+2+2sqrt(2))`
`=(2)/(2+sqrt(2))xx(2-sqrt(2))/(2-sqrt(2))=2-sqrt(2)`