Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Circle question

2008 · Shift 1 · Q38
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Advanced
  3. /Mathematics
  4. /Circle
  5. /2008 · Shift 1 · Q38

Circle question

2008 · Shift 1 · Q38

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 3x + y − 6=0\sqrt 3 x\, + \,y\, - \,6 = 03​x+y−6=0 and the point D is (3 32, 32)\left( {{{3\,\sqrt 3 } \over 2},\,{3 \over 2}} \right)(233​​,23​). 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
  1. A
    (x −23 )2+(y−1)2=1{\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1(x−23​)2+(y−1)2=1
  2. B
    (x −23 )2+(y+12)2=1{\left( {x\, - 2\sqrt 3 \,} \right)^2} + {(y + {1 \over 2})^2} = 1(x−23​)2+(y+21​)2=1
  3. C
    (x −3 )2+(y+1)2=1{\left( {x\, - \sqrt 3 \,} \right)^2} + {(y + 1)^2} = 1(x−3​)2+(y+1)2=1
  4. D
    (x −3 )2+(y−1)2=1{\left( {x\, - \sqrt 3 \,} \right)^2} + {(y - 1)^2} = 1(x−3​)2+(y−1)2=1
PreviousNext

More from Circle

  • 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 3​x+y−6=0 and the point D is (233​​,23​)…2008 · MCQ
  • 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 3​x+y−6=0 and the point D is (233​​,23​)…2008 · MCQ
  • Consider L1​:2x+3y+p−3=0L2​:2x+3y+p+3=0 where p is a real number, and C:x2+y2+6x−10y+30=0 STATEMENT-1 : If line L1​ is a…2008 · MCQ
  • Tangents are drawn from the point (17, 7) to the circle x2+y2=169. Statement 1 : The tangents are mutually perpendicular. Statement 2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle…2007 · MCQ
  • Let the straight line y=2x touch a circle with center (0,α),α>0, and radius r at a point A1​. Let B1​ be the point on the circle such that the line segment A1​B1​ is a diameter of the circle. Let α+r=5+5​… Includes table2024 · MCQ
  • Let A1​,A2​,A3​,…,A8​ be the vertices of a regular octagon that lie on a circle of radius 2 . Let P be a point on the circle and let PAi​ denote the distance between the points P and Ai​ for i=1,2,…,8. If P…2023 · Numerical
  • Let C1​ be the circle of radius 1 with center at the origin. Let C2​ be the circle of radius r with center at the point A=(4,1), where 1<r<3. Two distinct common tangents PQ and ST of C1​ and C2​ are drawn. The…2023 · Numerical
  • Let ABC be the triangle with AB=1,AC=3 and ∠BAC=2π​. If a circle of radius r>0 touches the sides AB,AC and also touches internally the circumcircle of the triangle ABC, then the value of r is ​…2022 · Numerical