Home
Class 11
MATHS
Perpendiculars are drawn, respectively, ...

Perpendiculars are drawn, respectively, from the points `Pa n dQ` to the chords of contact of the points `Qa n dP` with respect to a circle. Prove that the ratio of the lengths of perpendiculars is equal to the ratio of the distances of the points `Pa n dQ` from the center of the circles.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The length of chord of contact of the point (3,6) with respect to the circle x^(2)+y^(2)=10 is

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.

Prove that the tangent lines drawn from the outer point to the circle are equal? Or

If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove that they are equal.

Prove that the length of the tangents drawn from an external point to a circle are equal.

Prove that the length of the tangents drawn from an external point to a circle are equal.

Prove that the length of the tangents drawn from an external point to a circle are equal.

Prove that the length of the tangents drawn from an external point to a circle are equal.

Prove that the length of the tangents drawn from an external point to a circle are equal.

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. The number of such points (a+1,sqrt3a), where a is any integer, lying...

    Text Solution

    |

  2. A tangent is drawn to each of the circles x^2+y^2=a^2 and x^2+y^2=b^2d...

    Text Solution

    |

  3. Perpendiculars are drawn, respectively, from the points Pa n dQ to the...

    Text Solution

    |

  4. Find the locus of the midpoint of the chord of the circle x^2+y^2-2x-2...

    Text Solution

    |

  5. Find the center of the smallest circle which cuts circles x^2+y^2=1 an...

    Text Solution

    |

  6. A point moves so that the sum of the squares of the perpendiculars let...

    Text Solution

    |

  7. From a point P on the normal y=x+c of the circle x^2+y^2-2x-4y+5-lambd...

    Text Solution

    |

  8. The circle x^2+y^2-4x-4y+4=0 is inscribed in a variable triangle O A B...

    Text Solution

    |

  9. Consider three circles C1, C2 and C3 such that C2 is the director circ...

    Text Solution

    |

  10. The line 9x+y-18=0 is the chord of contact of the point P(h , k) wit...

    Text Solution

    |

  11. A circle x^2 +y^2 + 4x-2sqrt2 y + c = 0 is the director circle of circ...

    Text Solution

    |

  12. Tangents are drawn to the circle x^2+y^2=9 at the points where it is ...

    Text Solution

    |

  13. Find the length of the chord of contact with respect to the point on ...

    Text Solution

    |

  14. The distance between the chords of contact of tangents to the circle x...

    Text Solution

    |

  15. If 3x+y=0 is a tangent to a circle whose center is (2,-1) , then find ...

    Text Solution

    |

  16. Find the number of common tangent to the circles x^2+y^2+2x+8y-23=0 an...

    Text Solution

    |

  17. Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that ...

    Text Solution

    |

  18. Find the equation of the chord of the circle x^2+y^2=9 whose middle po...

    Text Solution

    |

  19. Find the circle of minimum radius which passes through the point (4, 3...

    Text Solution

    |

  20. A variable chord is drawn through the origin to the circle x^2+y^2-2a ...

    Text Solution

    |