Home
Class 12
MATHS
C1 and C2, are the two concentric circle...

`C_1 and C_2`, are the two concentric circles withradii `r_1 and r_2, (r_1 lt r_2)`. If the tangents drawnfrom any point of `C_2`, to `C_1`, meet again `C_2`, at theends of its diameter, then

A

`r_(2)=2r_(1)`

B

`r_(2)=sqrt(2)r_(1)`

C

`r_(2)^(2)lt 2r_(1)^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
In `Delta OPM`, we obtain
`sin 45^(@)=(OM)/(OP)rArr (1)/(sqrt(2))=(r_(1))/(r_(2))rArr r_(2)=sqrt(2)r_(1)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section-I (Solved MCQs)|1 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|53 Videos

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

C_1 and C_2 are fixed circles of radii r_1 and r_2 touches each other externally. Circle 'C' touches both Circles C_1 and C_2 extemelly. If r_1/r_2=3/2 then the eccentricity of the locus of centre of circles C is

The circle S_1 with centre C_1 (a_1, b_1) and radius r_1 touches externally the circle S_2 with centre C_2 (a_2, b_2) and radius r_2 If the tangent at their common point passes through the origin, then

Transverse common tangents are drawn from O to the two circles C_1,C_2 with 4, 2 respectively. Then the ratio of the areas of triangles formed by the tangents drawn from O to the circles C_1 and C_2 and chord of contacts of O w.r.t the circles C_1 and C_2 respectively is

If the sum of the areas of two circles with radii r_1 and r_2 is equal to the area of a circle of radius r , then r_1^2 +r_2^2 (a) > r^2 (b) =r^2 (c)

Given a circle of radius r . Tangents are drawn from point A and B lying on one of its diameters which meet at a point P lying on another diameter perpendicular to the other diameter. The minimum area of the triangle PAB is : (A) r^2 (B) 2r^2 (C) pir^2 (D) r^2/2

The radical axis of two circles having centres at C_(1) and C_(2) and radii r_(1) and r_(2) is neither intersecting nor touching any of the circles, if

Two circles centres A and B radii r_1 and r_2 respectively. (i) touch each other internally iff |r_1 - r_2| = AB . (ii) Intersect each other at two points iff |r_1 - r_2| ltAB lt r_1 r_2 . (iii) touch each other externally iff r_1 + r_2 = AB . (iv) are separated if AB gt r_1 + r_2 . Number of common tangents to the two circles in case (i), (ii), (iii) and (iv) are 1, 2, 3 and 4 respectively. circles x^2 + y^2 + 2ax + c^2 = 0 and x^2 + y^2 + 2by + c^2 = 0 touche each other if (A) 1/a^2 + 1/b^2 = 2/c^2 (B) 1/a^2 + 1/b^2 = 2/c^2 (C) 1/a^2 - 1/b^2 = 2/c^2 (D) 1/a^2 - 1/b^2 = 4/c^2

Let C_1 be the circle with center O_1(0,0) and radius 1 and C_2 be the circle with center O_2(t ,t^2+1),(t in R), and radius 2. Statement 1 : Circles C_1a n dC_2 always have at least one common tangent for any value of t Statement 2 : For the two circles O_1O_2geq|r_1-r_2|, where r_1a n dr_2 are their radii for any value of tdot

Two circles centres A and B radii r_1 and r_2 respectively. (i) touch each other internally iff |r_1 - r_2| = AB . (ii) Intersect each other at two points iff |r_1 - r_2| ltAB lt r_1+ r_2 . (iii) touch each other externally iff r_1 + r_2 = AB . (iv) are separated if AB gt r_1 + r_2 . Number of common tangents to the two circles in case (i), (ii), (iii) and (iv) are 1, 2, 3 and 4 respectively. If circles (x-1)^2 + (y-3)^2 = r^2 and x^2 + y^2 - 8x + 2y + 8=0 intersect each other at two different points, then : (A) 1ltrlt5 (B) 5ltrlt8 (C) 2ltrlt8 (D) none of these

In an acute angled triangle A B C , a semicircle with radius r_a is constructed with its base on BC and tangent to the other two sides. r_b a n dr_c are defined similarly. If r is the radius of the incircle of triangle ABC then prove that 2/r=1/(r_a)+1/(r_b)+1/(r_c)dot

OBJECTIVE RD SHARMA ENGLISH-CIRCLES-Section I - Solved Mcqs
  1. The locus of the centre of the circle passing through the intersection...

    Text Solution

    |

  2. Find the equation of the smallest circle passing through the point of ...

    Text Solution

    |

  3. C1 and C2, are the two concentric circles withradii r1 and r2, (r1 lt...

    Text Solution

    |

  4. The equation of a circle is x^2+y^2=4. Find the center of the smallest...

    Text Solution

    |

  5. From a point A(1, 1) on the circle x^(2)+y^(2)-4x-4y+6=0 two equal cho...

    Text Solution

    |

  6. The number of circles belonging to the system of circles 2(x^(2)+y^(2)...

    Text Solution

    |

  7. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

    Text Solution

    |

  8. If D,E and F are respectively, the mid-points of AB,AC and BC in Delta...

    Text Solution

    |

  9. In example 70, equations of the sides QR and RP are respectively

    Text Solution

    |

  10. A point on the line x=4 from which the tangents drawn to the circle 2(...

    Text Solution

    |

  11. The tangents PA and PB are drawn from any point P of the circle x^(2)+...

    Text Solution

    |

  12. Two concentric circles of which smallest is x^(2)+y^(2)=4, have the di...

    Text Solution

    |

  13. If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four poi...

    Text Solution

    |

  14. If two distinct chords, drawn from the point (p, q) on the circle x^2+...

    Text Solution

    |

  15. Let a and b be bonzero real numbers. Then the equation (ax^(2)+by^(2)+...

    Text Solution

    |

  16. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

    Text Solution

    |

  17. about to only mathematics

    Text Solution

    |

  18. If a >2b >0, then find the positive value of m for which y=m x-bsqrt(1...

    Text Solution

    |

  19. A circle circumscribing an equilateral triangle with centroid at (0,0)...

    Text Solution

    |

  20. Consider four circles (x+-1)^2+(y+-1)^2=1 . Find the equation of the s...

    Text Solution

    |