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IIT JEE 2008
Paper I


Formats Worksheet / Test Paper Quiz Review
: Multiple choice

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Paragraph of Question Nos. 15 to 17

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 √3x + y − 6 = 0 and the point D is

(
3√3

2
, 3

2
).

Further, it is given that the origin and the center of C are on the same side of the line PQ.


1.

15. The equation of circle C is

  (x − 2√3)2 + (y − 1)2 = 1

  (x − 2√3)2 + (y + 1/2)2 = 1

  (x − √3)2 + (y + 1)2 = 1

  (x − √3)2 + (y − 1)2 = 1

  Half-n-half Clue
 

2.

16. Points E and F are given by

 
( 3

2
, √3

2
), ( √3

2
, 1

2
)

 
(
√3

2
, 3

2
), (√3 , 0)

 
( 3

2
, 3

2
), ( √3

2
, 1

2
)

 
(
√3

2
, 1

2
), (√3 , 0)

  Half-n-half Clue
 

3.

17. Equations of the sides QR, RP are

 
y =
2

√3
x + 1 , y = − 2

√3
x − 1

 
y =
1

√3
x , y = 0

 
y =
√3

2
x + 1 , y = − √3

2
x − 1

  y = √3 x, y = 0

  Half-n-half Clue
 
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