Home
Class 11
MATHS
Let A B C be a given isosceles triangle ...

Let `A B C` be a given isosceles triangle with `A B=A C` . Sides `A Ba n dA C` are extended up to `Ea n dF ,` respectively, such that `B ExC F=A B^2dot` Prove that the line `E F` always passes through a fixed point.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE ENGLISH|Exercise All Questions|508 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|983 Videos

Similar Questions

Explore conceptually related problems

A B C is an isosceles triangle in which A B=A Cdot If Da n dE are the mid-points of A Ba n dA C respectively, prove that the points B ,C ,Da n dE are concylic.

A B C is an isosceles triangle in which A B=A C,B E\ a n d\ C F are its two medians. Show that B E=C Fdot

Let A B C be an isosceles triangle with A B=A C and let D ,\ E ,\ F be the mid points of B C ,\ C A\ a n d\ A B respectively. Show that A D_|_F E\ a n d\ A D is bisected by F E .

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

In Figure, A B C is an isosceles triangle with A B=A C ,\ B D\ a n d\ C E are two medians of the triangle. Prove that B D=C E

In an isosceles triangle A B C with A B=A C , a circle passing through B and C intersects the sides A Ba n dA C at Da n dE respectively. Prove that DE∣∣BC Bdot

In Figure, A B C is an isosceles triangle with A B=A C\ a n d\ m\ /_A B C=50^0dot Find m\ /_B D C\ a n d\ /_B E C

In triangle A B C ,points D , Ea n dF are taken on the sides B C ,C Aa n dA B , respectively, such that (B D)/(D C)=(C E)/(E A)=(A F)/(F B)=ndot Prove that triangle D E F=(n^2-n+1)/((n+1)^2) triangle(A B C)dot

Let A B C be an isosceles triangle in which A B=A C . If D ,\ E ,\ F be the mid-points of the sides B C ,\ C A\ a n d\ A B respectively, show that the segment A D\ a n d\ E F bisect each other at right angles.

In an isosceles triangle A B C with A B=A C , a circle passing through B\ a n d\ C intersects the sides A B\ a n d\ A C at D\ a n d\ E respectively. Prove that D E || B C .

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. Two sides of a rhombus lying in the first quadrant are given by 3x-4y=...

    Text Solution

    |

  2. The equation of straight line passing through (-2,-7) and having an in...

    Text Solution

    |

  3. Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA...

    Text Solution

    |

  4. A B C is an equilateral triangle with A(0,0) and B(a ,0) , (a>0). L, M...

    Text Solution

    |

  5. Let L1=0a n dL2=0 be two fixed lines. A variable line is drawn through...

    Text Solution

    |

  6. Find the points on y-axis whose perpendicular distance from the line ...

    Text Solution

    |

  7. Find all the values of theta for which the point (sin^2theta,sintheta)...

    Text Solution

    |

  8. If p and q are the lengths of perpendiculars from the origin to the ...

    Text Solution

    |

  9. The equations of two sides of a triangle are 3y-x-2=0a n dy+x-2=0. The...

    Text Solution

    |

  10. Prove that the lengths of the perpendiculars from the points (m^2,2m),...

    Text Solution

    |

  11. A triangle has two sides y=m1x and y=m2x where m1 and m2 are the root...

    Text Solution

    |

  12. The ratio in which the line 3x+4y+2=0 divides the distance between 3x+...

    Text Solution

    |

  13. Let A-=(6,7),B-=(2,3)a n dC-=(-2,1) be the vertices of a triangle. Fin...

    Text Solution

    |

  14. Find the equations of lines parallel to 3x-4y-5=0 at a unit distance f...

    Text Solution

    |

  15. Let P (sin theta, cos theta) (0 le theta le 2pi) be a point and let OA...

    Text Solution

    |

  16. Find the equation of a straight line passing through the point (-5,4) ...

    Text Solution

    |

  17. If A(x1, y1),B(x2, y2),C(x3, y3) are the vertices of a triangle, then...

    Text Solution

    |

  18. Are the points (3,4) and (2,-6) on the same or opposite sides of the l...

    Text Solution

    |

  19. Consider the equation y-y1=m(x-x1) . If m and x1 are fixed and differe...

    Text Solution

    |

  20. एक रेखा ऐसी है कि लाइनों 5 x − y + 4 = 0 तथा 3 x + 4 y − 4 = 0के बीच...

    Text Solution

    |