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Circle question

2008 · Shift 1 · Q39

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PYQ Library
JEE Advanced
Mathematics
Circle
2008 · Shift 1 · Q39

Circle question

2008 · Shift 1 · Q39

JEE AdvancedMathematicsCircleMCQ+3 / −1

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation

\sqrt 3 x\, + \,y\, - \,6 = 0

and the point D is

\left( {{{3\,\sqrt 3 } \over 2},\,{3 \over 2}} \right)

. Further, it is given that the origin and the centre of C are on the same side of the line PQ.Points E and F are given by

A
$\left( {{{\,\sqrt 3 } \over 2},\,{3 \over 2}} \right),\,\left( {\sqrt 3 ,\,0} \right)$
B
$\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right),\,\left( {\sqrt 3 ,\,0} \right)$
C
$\left( {{{\,\sqrt 3 } \over 2},\,{3 \over 2}} \right),\,\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right)$
D
$\left( {{{\,3} \over 2},\,{{\sqrt 3 } \over 2}} \right),\,\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right)$

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