# What is the condition for CONCURRENCE OF THREE LINES ? Please help soon .Thank you .

Three straight lines are said to be concurrent if they passes through a point i.e., they meet at a point. Thus, if three lines are concurrent the point of intersection of two lines lies on the third line.

The point of intersection of any two lines, which lie on the third line is called the point of concurrence.

$\\ \text{Let the equations of the three concurrent straight lines be}\\ a_1 x + b_1y + c_1 = 0 %u2026%u2026%u2026%u2026%u2026. (i)\\$

$a_2 x + b_2 y + c_2 = 0 %u2026%u2026%u2026%u2026%u2026. (ii) and$

$a_3 x + b_3 y + c_3 = 0 %u2026%u2026%u2026%u2026%u2026. (iii)$

For lines to be concurrent, condition is this:

$\left|\begin{array}{lll} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}\right|=0$

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