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JEE Advanced2008MathematicsStraight LinesActual

Paragraph: A circle C of radius 1 is inscribed in an equilateral P Q R . The points of contact of C with the sides P Q, Q R, R P are D, E, F respectively. The line P Q is given by the equation 3 x+y-6=0 and the point D is ( 3 3 2 , 3 2 ) . Further, it is given that the origin and the centre of C are on the same side of the line P Q . Question: Points E and F are given by

Options

  1. A( 3 2 , 3 2 ),( 3 , 0)
  2. B( 3 2 , 1 2 ),( 3 , 0)
  3. C( 3 2 , 3 2 ), ( 3 2 , 1 2 )
  4. D( 3 2 , 3 2 ), ( 3 2 , 1 2 )

Correct answer

A. ( 3 2 , 3 2 ),( 3 , 0)

Step-by-step solution

Slope of line joining centre of circle to point D = 3 2 -1 3 3 2 - 3 = 1 3 [makes an angle 30^ with X -axis] Points E and F will make angle 150^ and -90^ with X -axis. E and F are given by and aligned x- 3 150^ & = y-1 150^ =1 x- 3 (-90^ ) & = y-1 (-90^ ) =1 E & = ( 3 2 , 3 2 ) and F & =( 3 , 0) aligned

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