Home
Class 10
MATHS
In an equilateral A B C , A D|B C , ...

In an equilateral ` A B C` , `A D_|_B C` , prove that `A D^2=3\ B D^2`

Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    RD SHARMA ENGLISH|Exercise All Questions|420 Videos

  • TRIGONOMETRIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

In an equilateral triangle A B C if A D_|_B C , then

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

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

In fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

If A B C D is a quadrilateral in which A B C D and A D=B C , prove that /_A = /_B .

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 .

A point D is on the side B C of an equilateral triangle A B C such that D C=1/4\ B C . Prove that A D^2=13\ C D^2 .

If A B C is an equilateral triangle such that A D_|_B C , then A D^2= (a) 3/2D C^2 (b) 2\ D C^2 (c) 3\ C D^2 (d) 4\ D C^2

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 an equilateral triangle ABC, D is a point on side BC such that B D=1/3B C . Prove that 9A D^2=7A B^2 .

RD SHARMA ENGLISH-TRIANGLES-All Questions
  1. In a right A B C right-angled at C , if D is the mid-point of B...

    Text Solution

    |

  2. In a quadrilateral A B C D , /B=90^o , A D^2=A B^2+B C^2+C D^2 , pro...

    Text Solution

    |

  3. In an equilateral A B C , A D|B C , prove that A D^2=3\ B D^2

    Text Solution

    |

  4. A B D is a right triangle right-angled at A and A C|B D . Show t...

    Text Solution

    |

  5. A guy wire attached to a vertical pole of height 18m is 24m long an...

    Text Solution

    |

  6. An aeroplane leaves an airport and flies due north at a speed of 10...

    Text Solution

    |

  7. In each of the figures [4.222 (i)-(iv)] given below, a line segment...

    Text Solution

    |

  8. In A B C , points P and Q are on C A and C B , respectively s...

    Text Solution

    |

  9. In Figure, D E || C B . Determine A C and A E .

    Text Solution

    |

  10. In Figure, given that /\ A B C ~ /\ P Q R and quad\ ABCD ~ quad\ PQRS...

    Text Solution

    |

  11. In A B C , P and Q are points on sides A B and A C respectively s...

    Text Solution

    |

  12. In each of the following figures, you find two triangles. Indicate ...

    Text Solution

    |

  13. In /\ P Q R , M and N are points on sides P Q and P R respectively ...

    Text Solution

    |

  14. In A B C , P and Q are points on sides A B and A C respectively s...

    Text Solution

    |

  15. In Figure, /\ A M B ~ /\ C M D ; determine M D in terms of x ,\ y an...

    Text Solution

    |

  16. In A B C , the bisector of /A intersects B C in D . If A B=18 c m ...

    Text Solution

    |

  17. In Figure, l || m Name three pairs of similar triangles with proper ...

    Text Solution

    |

  18. In Figure, A B || D C Prove that (i)/\ D M U ~ /\ B M V (ii) D Mxx...

    Text Solution

    |

  19. A B C D is a trapezium in which A B D C . P and Q are points on...

    Text Solution

    |

  20. In A B C ,\ D and E are points on sides A B and A C respectively ...

    Text Solution

    |