Home
Class 12
MATHS
In a !ABC if a = 7 , b = 8 and c = 9 , t...

In a `!ABC` if a = 7 , b = 8 and c = 9 , then the length of the line joining B to the mid-points of AC is

A

6

B

7

C

5

D

none of these

Text Solution

Verified by Experts

Clearly, BE is a median of `Delta` ABC.
`thereforeBE^(2)=1/4(2a^(2)+2c^(2)-b^(2))=1/4(98+162-64)rArrBE=7`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise SOLVED MCQ|2 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA|Exercise Chapter Test|31 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

Find the slope of the line joining the points (7,5) and (9,7) :

Find the mid point of the line joining the points (7, 6) and (-3, -4) .

In triangle ABC , AB = 10 AC = 7 , BC = 9 then find the length find the length of the median drawn from point C to side AB .

In Delta ABC if a=7,b=8,c=9 then the distance from the vertex B to the centroid is

A B C D is a kite having A B=A D and B C=C D . Prove that the figure formed by joining the mid-points of the sides, in order, is a rectangle.

A(3,4),B(-3,0) and C(7,-4) are the vertices of a triangle.Show that the line joining the mid-points of AB and AC is parallel to BC and is half of it.

The vertices of a triangle ABC are A (2,3,1) , B(-2, 2,0), and C(0,1,-1). What is the magnitude of the line joining mid points of the sides AC and BC ?

The mid point of the line segment joining the points (-5, 7) and (-1, 3) is

The vertices of a triangleABC are A(2,3,1),B(-2,2,0) and C(0,1,-1) What is the magnitude of the line joining mid-points of the side AC and BC?

OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
  1. In a !ABC if r(1) = 36 , r(2) = 18 and r(3) = 12 , then the perimeter ...

    Text Solution

    |

  2. If in a Delta ABC, AD, BE and CF are the altitudes and R is the circum...

    Text Solution

    |

  3. In a !ABC if a = 7 , b = 8 and c = 9 , then the length of the line joi...

    Text Solution

    |

  4. If the perimeter of a triangle and the diameter of an ex-circle are eq...

    Text Solution

    |

  5. If D id the mid-point of the side BC of a triangle ABC and AD is perpe...

    Text Solution

    |

  6. ABC is a triangle. D is the middle point of BC. If AD is perpendicular...

    Text Solution

    |

  7. If the median of a triangle through A is perpendicular to AB, then

    Text Solution

    |

  8. In a !ABC , if r(1) =2r(2) =3r(3) , then a:b:c =

    Text Solution

    |

  9. In a !ABC if r(1)ltr(2)ltr(3), then

    Text Solution

    |

  10. In a !ABC if r(1) = 8, r(2) = 12 and r(3) = 24, then a =

    Text Solution

    |

  11. If I is the incentre of a DeltaABC such that angleA=60^(@), then AI =

    Text Solution

    |

  12. If I(1) is the centre of the escribed circle touching side BC of Delta...

    Text Solution

    |

  13. In a !ABC , if 2R + r = r(1) , then

    Text Solution

    |

  14. The sides of the triangle are sinalpha , cosalpha and sqrt(1+sinalphac...

    Text Solution

    |

  15. In a !ABC , if 3a = b + c , then cot B/2 cot C/2 =

    Text Solution

    |

  16. In !ABC , if sin^(2)A/2,sin^(2)B/2,sin^(2)C/2 be in H.P., then a , b ,...

    Text Solution

    |

  17. In a !ABC , if 1/(b+c)+1/(c+a)=3/(a+b+c), then angleC=

    Text Solution

    |

  18. Observe the following statements: (I) In !ABC,bcos^(2)C/2+ccos^(2)B/2=...

    Text Solution

    |

  19. In a triangle , if r(1) = 2r(2) = 3r(3), then a/b + b/c + c/a is equa...

    Text Solution

    |

  20. Sides a , b , c of !ABC are in A.P. and costheta(1)=a/(b+c)costheta(2)...

    Text Solution

    |