# If the lines ax + 12y + 1 = 0, bx + 13y + 1 = 0 and cx + 14y – 1 = 0 are concurrent, then a, b, c are inA. H.P.B. G.P.C. A.P.D. none of these

The given lines are

ax + 12y + 1 = 0 … (1)

bx + 13y + 1 = 0 … (2)

cx + 14y + 1 = 0 … (3)

It is given that (1), (2) and (3) are concurrent. a(13 – 14) – 12(b – c) + 14b – 13c = 0

-a – 12b + 12c + 14b – 13c = 0

-a + 2b – c = 0

2b = a + c

Hence, a, b and c are in AP.

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