Home
Class 11
MATHS
Three circles touch each other externall...

Three circles touch each other externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 4. Then, the ratio of their product of radii to the sum of the radii is

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

Three circles with radius r_(1), r_(2), r_(3) touch one another externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 2 . The value of ((r_(1)r_(2)r_(3))/(r_(1)+r_(2)+r_(3))) is equal to

Three circles whose radii are a,b and c and c touch one other externally and the tangents at their points of contact meet in a point. Prove that the distance of this point from either of their points of contact is ((abc)/(a+b+c))^(1/2) .

Two circles touch each other externally. The sum of their areas is 58pi cm^(2) and the distance between their centres is 10 cm. Find the radii of the two circles.

Two circles touch each other internally. Show that the tangents drawn to the two circles from any point on the common tangent, are equal in length.

Circles with radii 3, 4 and 5 touch each other externally. If P is the point of intersection of tangents to these circles at their points of contact, then if the distance of P from the points of contact is lambda then lambda_2 is _____

Circles of radii 3,4,5 touch each other externally . Let P be the point of intersection of tangents of these circles at their points of contact .Show that the distance of P from a point of contact is sqrt5 .

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

Three circles touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm.

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

    Text Solution

    |

  2. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a3+x)+ ........+ 1/(2^(n-1)...

    Text Solution

    |

  3. Three circles touch each other externally. The tangents at their point...

    Text Solution

    |

  4. Prove that tan20^0tan40^0tan80^0=tan60^0

    Text Solution

    |

  5. If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(...

    Text Solution

    |

  6. The solution of the system of equations sinxsiny=(sqrt(3))/4,cosxcosy=...

    Text Solution

    |

  7. Find the least value of sec A+secB+secC in an acute angled triangle

    Text Solution

    |

  8. If in triangle A BC ,cosAcosB+sinAsinBsinC=1. Show that a : b : c=1:1:...

    Text Solution

    |

  9. Let f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x) for some real numbe...

    Text Solution

    |

  10. Number of values of p for which equation sin^3x+1+p^3-3 p sinx=0 (p >0...

    Text Solution

    |

  11. In A B C , prove that cosA+cosB+cosClt=3/2dot

    Text Solution

    |

  12. In a DeltaABC, the median to the side BC is of length 1/sqrt(11-6sqrt...

    Text Solution

    |

  13. If pcos e ctheta+qcottheta=2 and p^2cos e c^2theta-q^2cot^2theta=5 t...

    Text Solution

    |

  14. In a /\A B C , if tanA/2,tanB/2,tanC/2"are in"AdotPdot, then show t...

    Text Solution

    |

  15. With usual notion, if in triangle A B C , (b+c)/(11)=(c+a)/(12)=(a+b)...

    Text Solution

    |

  16. alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, resp...

    Text Solution

    |

  17. Solution of the equation sin(sqrt(1+sin2theta))=sintheta+costhetai s(n...

    Text Solution

    |

  18. If in a Delta ABC, cosA+ cosB + cosC =3/2. Prove that DeltaABC is an e...

    Text Solution

    |

  19. Let alpha,beta,gamma>0a n dalpha+beta+gamma=pi/2dot Then prove that sq...

    Text Solution

    |

  20. In DeltaABC,BC=1,sin.(A)/2=x1,sin.(B)/2=x2,cos.(A)/2=x3andcos.(B)/2=x4...

    Text Solution

    |