Show that the following lines are concurrent: `L_1=(a-b)x+(b-c)y+(c-a)=0` `L_2=(b-c)x+(c-a)y+(a-b)=0` `L_3=(c-a)x+(a-b)y+(b-c)=0`

Explanation

Given,`(a−b)x+(b−c)y+a−c=0`

`(b−c)x+(c−a)y+b−a=0`

`(c−s)x+(a−b)y+c−b=0`

For these to be concurrent

​`|[a−b, b−c, c−a],[​b−c, c−a , a−b],[
a−c, b−a, c−b]|​=0 `


`R_1​→R_1​+R_2​+R_3`

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