Home
Class 10
MATHS
If A B C is a right triangle right-angl...

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`

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

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, triangle A B C is right-angled at Bdot Give that A B=9C M ,\ A C=15 C M ,\ a n d\ D ,\ E\ are the mid-points of the sides A B\ a n d\ A C respectively, calculate The length of B C (ii) The area of A D E

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r\ (B Y X D)=2\ a r\ (\ M B C)

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r\ (C Y X E)=2a r(\ F C B)

A B C is a triangle in which D is the mid-point of B C ,\ E\ a n d\ F are mid-points of D C\ a n d\ A E respectively. If area of A B C is 16\ c m^2, find the area of D E F

If in a triangle ABC, right angle at B,s-a=3 and s-c=2, then a=2,c=3 b.a=3,c=4 c.a=4,c=3 d.a=6,c=8

In a A B C if D\ a n d\ E are mid-points of B C\ a n d\ A D respectively such that a r\ ( A E C)=4\ c m^2 , then a r\ ( B E C)= 4\ c m^2 (b) 6\ c m^2 (c) 8\ c m^2 (d) 12 c m^2

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

In a triangle A B C , right angled at B , the inradius is (A B+B C-A C)/2 (b) (A B+A C-B C)/2 (A B+B C+A C)/2 (d) none

In Figure, M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B C respectively. If M N=3c m ,\ N P=3. 5 c m\ a n d\ M P=2. 5 c m , calculate B C ,\ A B\ a n d\ A C

RD SHARMA-TRIANGLES-All Questions
  1. ABC is a right triangle right-angled at B. Let D and E be any points o...

    Text Solution

    |

  2. A girl of height 90 cm is walking away from the base of a lamp-post...

    Text Solution

    |

  3. If A B C is a right triangle right-angled at Ba n dM ,N are the mid-...

    Text Solution

    |

  4. Determine whether the triangle having sides (a-1)c m ,2sqrt(a)c m and ...

    Text Solution

    |

  5. If triangle A B C is similar to triangle D E F such that B C=3C M ...

    Text Solution

    |

  6. The perimeters of two similar triangles are 30cm and 20cm respectively...

    Text Solution

    |

  7. Two triangles B A Ca n dB D C , right angled at Aa n dD respectively, ...

    Text Solution

    |

  8. ABC is a right angle triangle right angled at A. A circle is inscribed...

    Text Solution

    |

  9. In Figure, /B A C=90^0,A D is its bisector. If D E|A c , prove that D...

    Text Solution

    |

  10. Prove that the line segments joints joining the mid-points of the a...

    Text Solution

    |

  11. In figure, P is the mid-point of B C , ,Q is the mid-point of A P ,...

    Text Solution

    |

  12. A vertical stick 12m long casts a shadow 8m long on the ground. At the...

    Text Solution

    |

  13. In a quadrilateral A B C D , if bisectors of the /A B Ca n d/A D C mee...

    Text Solution

    |

  14. In A B C , the bisector of /B meets A C at Ddot A line P Q A C meets...

    Text Solution

    |

  15. The bisectors of the angles B and C of a triangle A B C , meet the o...

    Text Solution

    |

  16. In A B C ,/B=2/C and the bisector of /B intersects A C at Ddot Prove ...

    Text Solution

    |

  17. In Figure, D E B C , if A D=x ,D B=x-2,A E=x+2 and E C=x-1, find the ...

    Text Solution

    |

  18. Lex X by any point on the side BC of a triangle ABC. If XM, XN are d...

    Text Solution

    |

  19. In Figure P Q is parallel to M Ndot if (K P)/(P M)=4//13 and K N=20. 4...

    Text Solution

    |

  20. In Figure D E B C and C D E Fdot Prove that A D^2=A BxA Fdot

    Text Solution

    |