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Question

If in a ΔABC, A(1,10), circumcentre (13,23) and orthocentre (113,43), then the equation of side BC is

A
12x+39y+155=0
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B
12x39y+155=0
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C
12x+39y155=0
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D
12x39y155=0
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Solution

The correct option is D 12x39y155=0
Given, circumcentre, S(13,23)
orthocentre, H(113,43)
We know that centroid divides the circumcentre and orthocentre in the ratio of 1:2
G⎜ ⎜ ⎜ ⎜1×113+2(13)1+2,1(43)+2(23)1+2⎟ ⎟ ⎟ ⎟G(1,89)

Let D(x,y) is the mid-point of B and C
G divides AD in 2:1, so
2x+13=1, 2y+103=89x=1, y=113D(1,113)

Now as we know that line AHBC
Hence equation for side BC
y+113=⎜ ⎜ ⎜11131043⎟ ⎟ ⎟(x1)y+113=413(x1)12x39y155=0

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