Home
Class 10
MATHS
If A B C is an isosceles triangle and...

If `A B C` is an isosceles triangle and `D` is a point on `B C` such that `A D_|_B C` , then `A B^2-A D^2=B DdotD C` (b) `A B^2-A D^2=B D^2-D C^2` (c) `A B^2+A D^2=B DdotD C` (d) `A B^2+A D^2=B D^2-D C^2`

Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    RD SHARMA|Exercise All Questions|417 Videos
  • TRIGONOMETRIC IDENTITIES

    RD SHARMA|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

In an equilateral triangle A B C if A D_|_B C , then A D^2 = (a)C D^2 (b) 2C D^2 (c) 3C D^2 (d) 4C D^2

A B D is a right triangle right-angled at A and A C_|_B D . Show that A B^2=B CdotB D (ii) A C^2=B CdotD C (iii) A D^2=B DdotC D (iv) (A B^2)/(A C^2)=(B D)/(D C)

In Figure, ABD is a triangle right-angled at A and A C_|_B D . Show that (i) A B^2=B C.B D (ii) A C^2=B C.D C (iii) A D^2=B D.C D

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

In figure, O is a point in the interior of a triangle ABC, O D_|_B C ,O E_|_A C and O F_|_A B . Show that (i) O A^2+O B^2+O C^2-O D^2-O E^2-O F^2=A F^2+B D^2+C E^2 (ii) A F^2+B D^2+C E^2=A W^2+C D^2+B F^2

In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C^2 .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

In figure, ABC is triangle in which /_A B C > 90o and A D_|_C B produced. Prove that A C^2=A B^2+B C^2+2B C.B D .

RD SHARMA-TRIANGLES-All Questions
  1. In a A B C , A D is the bisector of /B A C . If A B=8c m , B D=6c ...

    Text Solution

    |

  2. A B C D is a trapezium such that B C || A D and A B=4c m . If the ...

    Text Solution

    |

  3. If A B C is an isosceles triangle and D is a point on B C such t...

    Text Solution

    |

  4. A B C is a right triangle right-angled at A and A D|B C . Then, (B ...

    Text Solution

    |

  5. If E is a point on side C A of an equilateral triangle A B C suc...

    Text Solution

    |

  6. If in A B C and D E F , (A B)/(D E)=(B C)/(F D) , then A B C ~ D E...

    Text Solution

    |

  7. If in two triangles A B C and D E F , (A B)/(D E)=(B C)/(F E)=(C A)...

    Text Solution

    |

  8. A B C D E F , a r( A B C)=9c m^2 , a r( D E F)=16 c m^2 . If B C=2. ...

    Text Solution

    |

  9. The length of the hypotenuse of an isosceles right triangle whose o...

    Text Solution

    |

  10. A man goes 24m due west and then 7m due north. How far is he from t...

    Text Solution

    |

  11. A B C D E F . If B C=3c m , E F=4c m and a r( A B C)=54 c m^2 , then...

    Text Solution

    |

  12. A B C P Q R such that a r( A B C)=4a r( P Q R)dot If B C=12 c m , th...

    Text Solution

    |

  13. The areas of two similar triangles are 121\ c m^2 and 64\ c m^2 res...

    Text Solution

    |

  14. If A B C D E F such that D E=3c m , E F=2c m , D F=2. 5 c m , B C=4...

    Text Solution

    |

  15. In an equilateral triangle A B C if A D|B C , then 5A B^2=4A D^2 (b...

    Text Solution

    |

  16. If A B C D E F such that A B=9. 1 c m and D E=6. 5 c m . If the ...

    Text Solution

    |

  17. In an isosceles triangle A B C if A C=B C and A B^2=2A C^2 , then /...

    Text Solution

    |

  18. A B C is an isosceles triangle in which /C=90o . If A C=6c m , then...

    Text Solution

    |

  19. If in two triangles A B C and D E F , /A=/E ,\ \ /B=/F , then wh...

    Text Solution

    |

  20. In an isosceles triangle A B C , if A B=A C=25 c m and B C=14 c m ,...

    Text Solution

    |