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Question

The polar coordinates of the vertices of a triangle are (0,0), (3,π2) and (3,π6). Then the triangle is

A
right angled
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B
isosceles
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C
equilateral
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D
none of these
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Solution

The correct option is C equilateral
Given A(0,0),B(3,π2),C(3,π6)
d=r21+r222r1r2cos(θ1θ2)
AB=0+90=3
BC=9+918cos(π3)
BC=3
AC=0+90=3
AB=BC=AC
Hence, the triangle is equilateral.

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