The distance between the orthocentre and circumcentre of a triangle whose vertices are P(3,0),Q(0,0) and R(32,−3√32) is
A
0
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B
√2
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C
√3
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D
3√3
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Solution
The correct option is A0 P(3,0),Q(0,0) and R(32,−3√32) ∴PQ=√(3−0)2+(0−0)2=3 QR=
⎷(32−0)2+(−3√32−0)2=3 PR=
⎷(3−32)2+(0+3√32)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.