Home
Class 11
MATHS
If D is the mid point of side BC of a tr...

If D is the mid point of side BC of a triangle ABCand AD is perpendicular to BC, then

A

`3a^2=b^2-3c^2`

B

`3b^2=a^2-c^2`

C

`b^2=a^2-c^2`

D

`a^2+b^2=5c^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • SETS AND RELATIONS

    PATHFINDER|Exercise QUESTION BANK|56 Videos

  • STATISTICS

    PATHFINDER|Exercise QUESTION BANK|45 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC, D is the mid point of side BC . If AD is perpendicular to AC . then prove that cosA cosC =(2(c^2-a^2))/(3ca)

If D is the mid-pointof the side BC of a triangle ABC and angleBAD = theta, angleCAD = phi , then show that cot theta - cot phi = cot B - cot C .

E is the mid point of side OB of triangle OAB . D is a point on AB such that AD : DB = 2 : 1 . If OD and AE intersect at P , then -

ABC is a triangle and D is the middle point of BC. If AD is perpendicular to AC, prove that, cosA cos C =(2(c^(2)-a^(2))/(3ca))

In a DeltaABC , the point D divides BC in the ratio 1:2 Also AD is perpendicular to AB. Then the value of the expression tanB(1+2tanAtanc)-2tanC is:

D is the mid-point of the side BC of the DeltaABC and P is any point on BC. Let us join P, A. The line segment drawn through D, parallel to PA intersects AB at Q. Prove that DeltaBPQ=1/2DeltaABC .

O is the circumcentre of Delta ABC and OD is perpendicular on the side BC, prove that angle BOD= angle BAC

Delta ABC is an obtus triangle in which /_B = obtus angle. If AD is perpendicular to BC ( or extended BC ) ,then prove that AC^(2) = AB^(2) +BC^(2) + 2BC xx BD .

PATHFINDER-SOLUTION OF TRIANGLE AND HEIGHT AND DISTANCE-QUESTION BANK
  1. If the area of a triangle ABC is given by Delta=a^2-(b-c)^2then tan(A...

    Text Solution

    |

  2. If in a DeltaABC, cosA+2cosB+cosC=2,then a,b,c are in

    Text Solution

    |

  3. If D is the mid point of side BC of a triangle ABCand AD is perpendicu...

    Text Solution

    |

  4. If f,g,h are the internal bisectors of a DeltaABC then 1/fcos(A/2)+1/...

    Text Solution

    |

  5. If a,b,c,d be the sides of a quadrilateral and g(x)=f[f{f(x)}], where ...

    Text Solution

    |

  6. In aDeltaABC,sinA/sinC=sin(A-B)/sin(B-C)then

    Text Solution

    |

  7. Let a,b,c be the sides of triangle whose perimeter is p and area is A,...

    Text Solution

    |

  8. If in a DeltaABC, CD is the angle bisector of the angleABC, then CD is...

    Text Solution

    |

  9. If A, A1,A2,A3 are the areas of the inscribed and escribed circles of ...

    Text Solution

    |

  10. If A+B =pi/3 and cosA+cosB=1, then which of the following is/are true

    Text Solution

    |

  11. When any two sides and one of the opposite acute are given, under cert...

    Text Solution

    |

  12. When any two sides and one of the opposite acute are given, under cert...

    Text Solution

    |

  13. If p1,p2,p3 are altitudes of a triangle ABC from the vertices A,B,C re...

    Text Solution

    |

  14. If p1,p2,p3 are altitudes of a triangle ABC from the vertices A,B,C re...

    Text Solution

    |

  15. Match List - I with List-II

    Text Solution

    |

  16. Match List - I with List-II

    Text Solution

    |

  17. In a Delta, (a+b+c)(b+c-a)=lambdabc, whenlambda inI, then greatest va...

    Text Solution

    |

  18. In a Delta ABC then line joining the circumcentre to the incentre is p...

    Text Solution

    |

  19. If in a DeltaABC, a=5, b=4 and cos(A-B)=31/32, then the third side c ...

    Text Solution

    |

  20. In DeltaABC, if BC is unity, sin(A/2)=x1,sin(B/2)=x2,cos(A/2)=x3,cos(B...

    Text Solution

    |