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Question

The distance between the orthocentre and circumcentre of a triangle whose vertices are P(3,0),Q(0,0) and R(32,332) is

A
0
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B
2
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C
3
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D
33
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Solution

The correct option is A 0
P(3,0),Q(0,0) and R(32,332)
PQ=(30)2+(00)2=3
QR= (320)2+(3320)2=3
PR= (332)2+(0+332)2=3

Hence, PQ=QR=PR
So, the triangle is equilateral.
Now, since in an equilateral triangle orthocentre and circumcentre coincides, therefore distance between them is zero.

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