Home
Class 10
MATHS
In right-angled triangle A B C in wh...

In right-angled triangle `A B C` in which `/_C=90^@` , if `D` is the mid-point of `B C` , prove that `A B^2=4\ A D^2-3\ A C^2` .

Text Solution

AI Generated Solution

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 a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

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

In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A E_|_B C . Prove that: (i) A B^2=A D^2-B C* D E+1/4B C^2

A B C is a right angled triangle in which /_A=90^0a n d\ A B=A Cdot Find /_B\ a n d\ /_C

A B C is a right-angled triangle is which /_A=90^0a n d\ A B=A Cdot Find /_B\ a n d\ /_C

In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A E_|_B C . Prove that: (i) A B^2=A D^2-B C . D E+1/4B C^2 (ii) A B^2+A C^2=2\ A D^2+1/2B C^2

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C . GIVEN : A A B C in which /_B=90^0 and D is the mid-point of A Cdot TO PROVE : B D=1/2A C CONSTRUCTION Produce B D to E so that B D=D Edot Join E Cdot

If A B C is a right triangle right-angled at Ba n dM ,N are the mid-points of A Ba n dB C respectively, then 4(A N^2+C M^2)= (A) 4A C^2 (B) 5A C^2 (C) 5/4A C^2 (D) 6A C^2

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A D . Prove that area of B E D = 1/4 area of ABC.

RD SHARMA ENGLISH-TRIANGLES-All Questions
  1. In an acute angled triangle , express a median in term of its sides.

    Text Solution

    |

  2. Calculate the height of an equilateral triangle each of whose sides...

    Text Solution

    |

  3. In right-angled triangle A B C in which /C=90^@ , if D is the ...

    Text Solution

    |

  4. In Fig. 4.220, D is the mid-point of side B C and A E|B C . If B...

    Text Solution

    |

  5. In Fig. 4.221, /B<90o and segment A D|B C , show that b^2=h^2+a^...

    Text Solution

    |

  6. In A B C , /A is obtuse, P B|A C and Q C|A B . Prove that: A BxxA ...

    Text Solution

    |

  7. In a right A B C right-angled at C , if D is the mid-point of B...

    Text Solution

    |

  8. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |