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Question

If in a triangle A=(1,10), circumcentre =(−13,23) and orhocentre =(113,43) then the co-ordinate of mid-point of side opposite to A is

A
(1,6)
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B
(1,5)
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C
(1,3)
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D
(1,113)
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Solution

The correct option is C (1,113)
Given points are A(1,1,0) and Circumcenter(C) (13,23) and orthocenter(O) (113,43)

Using mid point theorem, to find the centre(G) of the circumcenter and the orthocenter,

we get

G(1,89)

Now let D be the mid point of side BC (oppposite to A), since G is the mid point of AD where coordinates of A(1,1,0) and D(x,y). So, we find the coordinate of D(x,y)

2x+13=1,

2y+103=89

x=1,y=113

D(x,y)=(1,113)

which is the mid point of the side opposite to A.

hence, option (D) is correct.

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