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Question

The equations of the perpendicular bisectors of the sides AB and AC of a triangle ABC are xy+5=0 and x+2y=0 respectively. If the co-ordinates of A are (1,2), then the equation of BC is


A
23x+14y40=0
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B
14x+23y40=0
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C
23x14y+40=0
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D
None of these
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Solution

The correct option is B 14x+23y40=0
AB line is perpendicular to EO(perpendicular bisector to side AB) and passes through vertex A, Equation of AB::x+y+1=0
Coordinates of E=(x1+12,y122)
Which is also intersection point of AB with xy+5=0(EO line equation)
So,
x1+12=3; y122=2(x1,y1)(7,6)
similarly equation of AC::y=2x4
and coordinates of F=(x2+12,y222)
Which is also intersection point of AC with x+2y=0(F0 line equation)
So,
x2+12=85; y222=45(x2,y2)(11/5,2/5)
So, the equation of sideBC:
y6=2/5611/5+7(x+7)14x+23y40=0

Mathematics

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