Show that the straight lines `L_1=(b+c)x+a y+1=0,\ L_2=(c+a)x+b y+1=0\ n d\ L_3=(a+b)x+c y+1=0\ ` are concurrent.

Explanation

The given lines can be written as follows: (`b + c) x + ay + 1 = 0 … (1)`

` (c + a) x + by + 1 = 0 … (2)`

` (a + b) x + cy + 1 = 0 … (3)`

The equations can easily b reduced by determinant form and thus their determinant is zero


or,`|[b+c,a,1],[c+a,b,1],[a+b,c,1]|`

`|[b+c,a,1],[c+a,b,1],[a+b,c,1]|=0`

Hence proved, the given lines are concurrent.
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