IIT-JEE 2008 Paper 1 Offline | Circle Question 27 | Mathematics

1

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+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.

Equations of the sides QR, RP are

A

$$y = {2 \over {\sqrt 3 }}\,x + \,1,\,\,y = \, - {2 \over {\sqrt 3 }}\,x - 1$$

B

$$y = {1 \over {\sqrt 3 }}\,x,\,\,y = \,0$$

C

$$y = {{\sqrt 3 } \over 2}\,x + \,1,\,\,y = \, - {{\sqrt 3 } \over 2}\,x - 1$$

D

$$y = \sqrt 3 \,x,\,\,y = \,0$$

2

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+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

$$\left( {{{\,3} \over 2},\,{{\sqrt 3 } \over 2}} \right),\,\left( {{{\,\sqrt 3 } \over 2},\,{1 \over 2}} \right)$$

3

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+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.

The equation of circle C is

A

$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$

B

$${\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y + {1 \over 2})^2} = 1$$

C

$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y + 1)^2} = 1$$

D

$${\left( {x\, - \sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1$$

4

IIT-JEE 2007 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Let $$\mathrm{ABCD}$$ be a quadrilateral with area 18 , with side $$\mathrm{A B}$$ parallel to the side $$\mathrm{C D}$$ and $$\mathrm{A B}=2 \mathrm{CD}$$. Let $$\mathrm{AD}$$ be perpendicular to $$\mathrm{AB}$$ and $$\mathrm{CD}$$. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is :

A

3

B

2

C

$$\frac{3}{2}$$

D

1

JEE Advanced Subjects