Home
Class 12
MATHS
If the points (a, 0), (b,0), (0, c), and...

If the points `(a, 0), (b,0), (0, c)`, and `(0, d)` are concyclic `(a, b, c, d > 0)`, then prove that `ab = cd`.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    CENGAGE PUBLICATION|Exercise All Questions|238 Videos

Similar Questions

Explore conceptually related problems

The points (-a,-b).(0,0),(a,b) and (a^2, ab) are

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

Consider the points A(0, 0, 0), B(5, 0, 0), C(3, 0, 4) and D(0, 4, 3). The points A, B, C and D are-

The points (-a,-b),(a,b),(0,0) and (a^(2),ab), a ne 0, b ne 0 are always

If a/(b +c) = b/(c+a) = c/(a+b) " and " a + b + c ne 0 , then prove that a = b = c .

Consider the points A(0, 0, 0), B(5, 0, 0), C(3, 0, 4) and D(0, 4, 3). The line AC and BD are-

If a , b > 0 a n d 0 < p < 1, then prove that (a+b)^p < a^p+b^pdot

If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is

Consider the points A(0, 0, 0), B(5, 0, 0), C(3, 0, 4) and D(0, 4, 3). Area of triangle ABC (in square units) is -

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the orthocentre of A B C with vertices A(1,0),B(-2,1), and C(...

    Text Solution

    |

  2. If (b2-b1)(b3-b1)+(a2-a1)(a3-a1)=0 , then prove that the circumcente...

    Text Solution

    |

  3. If line 3x-a y-1=0 is parallel to the line (a+2)x-y+3=0 then find ...

    Text Solution

    |

  4. If A(2,-1)a n dB(6,5) are two points, then find the ratio in which t...

    Text Solution

    |

  5. Angle of a line with the positive direction of the x-axis is theta ....

    Text Solution

    |

  6. Let A(6,4)a n dB(2,12) be two given point. Find the slope of a line ...

    Text Solution

    |

  7. If the points (a, 0), (b,0), (0, c), and (0, d) are concyclic (a, b, c...

    Text Solution

    |

  8. If A(-2,1),B(2,3)a n dC(-2,-4) are three points, find the angle betwee...

    Text Solution

    |

  9. The line joining the points (x ,2x)a n d(3,5) makes an obtuse angle...

    Text Solution

    |

  10. If the line passing through (4,3)a n d(2,k) is parallel to the line...

    Text Solution

    |

  11. Find the area of the pentagon whose vertices are A(1, 1), B(7,21), C(7...

    Text Solution

    |

  12. If A = (3, 4) and B is a variable point on the lines |x| = 6 If AB le ...

    Text Solution

    |

  13. The three points (-2, 2), (8, -2) and (-4,-3) are the vertices of :

    Text Solution

    |

  14. The points (-a ,-b),(a , b),(a^2,a b) are (a) vertices of an equ...

    Text Solution

    |

  15. The distance between the point (acosalpha,asinalpha) and (acosbeta,asi...

    Text Solution

    |

  16. Find the length of altitude through A of the triangle A B C , where...

    Text Solution

    |

  17. A and B are points (3,4) and (5,-2), find the co-ordinate of the point...

    Text Solution

    |

  18. If the point (0,0),(2,2sqrt(3)), and (p,q) are the vertices of an eq...

    Text Solution

    |

  19. If sum(i=1)^(2n) sin^-1xi = npi then find the value of sum(i = 1)^(2n)...

    Text Solution

    |

  20. If the vertices of a triangle have rational coordinates, then prove...

    Text Solution

    |