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Two equal sides of an isosceles triangle are given by the equation 7x - y + 3 = 0 and x + y -3 = 0 and its third side passes through the point (1, -10). The equation of the third side can be

(A)  x + 3y + 29 = 0

(B)  x - 3y = 31

(C)  3x + y = 3

(D)  3x + y + 7 = 0

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Correct option  (B)(D)

Explanation:

∴ third side will be parallel to bisectors of two given line

∴  Bisectors are 7x - y + 3/5√2 = ±(-x - y + 3)/√2

∴ Bisectors are 3x + y - 1 = 0 and x -3y + 9 = 0

Now required third side will be parallel to these bisectors 

3x + y + 7 = 0 or x - 3y - 31 = 0

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