Home
Class 11
MATHS
Perpendicular drawn from the vertices A,...

Perpendicular drawn from the vertices A,B,C upon opposite sides of `triangle ABC` passes through a fixed point O.if `bar(OA)=x.bar(OB)=y` and ` bar(OC)=z` then prove that `a/x+b/y+c/z=(abc)/(xyz)`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION AND INVERSE

    PATHFINDER|Exercise QUESTION BANK|195 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    PATHFINDER|Exercise QUESTION BANK|241 Videos

Similar Questions

Explore conceptually related problems

The perpendicular from the vertices A, B and C of a triangle ABC on the opposite sides meet at O. If OA=x, OB=y and OC=z, prove that, a/x + b/y + c/z = (abc)/(xyz) .

Prove analytically that in any triangle the perpendiculars drawn from the vertices upon the opposite sides are concurrent.

If in Delta ABC , the distance of the vertices from the orthocenter are x,y, and z then prove that (a)/(x) + (b)/(y) + (c)/(z) = (abc)/(xyz)

If a^(x)=b^(y)=c^(z) and b^(2)=ac prove that (1)/(x)+(1)/(z)=(2)/(y)

If a^x=b^y=c^z" and "abc=1 , then prove that xy+yz+zx=0 .

If b+c-a/x+y-x = c+a-b/c+x-y = a+b_c/x+y-z, then prove that a/x = b/y = c/z.

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

If x+z = 2y " and " b^2 = ac , then prove that a^(y-z)*b^(z-x)*c^(x-y) =1 .

If h be the length of the perpendicular drawn from A on BC in the triangle ABC, show that, h=(a sin B sin C)/(sin(B+C)) .

If the points A(z),B(-z),C(1-z) are the vertices of an equilateral triangle ABC then Re(z) is

PATHFINDER-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. In any triangle ABC prove that a^2cotA+b^2cotB+c^2cotC=(abc)/R

    Text Solution

    |

  2. in any triangle ABC prove that (b-c)/acos^2(A/2)+(c-a)/(b)cos^2(B/2)+(...

    Text Solution

    |

  3. In triangle ABC if the angles A,B and C be in A.P. then show that 2co...

    Text Solution

    |

  4. In triangle ABC if cosAcosB +sinAsinB sinC=1 then prove that a:b:c=1:1...

    Text Solution

    |

  5. In triangleABC (b+c)/11=(c+a)/12=(a+b)/13 then prove that (cosA)/7=(co...

    Text Solution

    |

  6. in triangleABC if (a^2+b^2)/(a^2-b^2)=sin(A+B)/sin(A-B) then prove th...

    Text Solution

    |

  7. In triangleABC if a/(b+c)=tan(A/2) the show that A+C=pi/2

    Text Solution

    |

  8. if the lengths of sides of a triangle be 1-2x,(x^2-x+1 and (x^2-1) the...

    Text Solution

    |

  9. If in triangleABC ,sin^4A+sin^4B+sin^4C=sin^2Bsin^2C+2sin^2Csin^2A+2si...

    Text Solution

    |

  10. For any triangle ABC prove that acosA+bcosB +c cosC=2a sinBsinC

    Text Solution

    |

  11. If in triangle ABC ,b^2=a(c+a) and c^2=(a+b)b then prove that cosAcos ...

    Text Solution

    |

  12. If in triangle ABC cosA+cosB+cosC=3/2 then prove that triangle is equi...

    Text Solution

    |

  13. If 8R^2=a^2+b^2+c^2 then show that the triangle is right angled

    Text Solution

    |

  14. If in a triangle ABC ,atanA +btan B =(a+b)tan((A+B)/2) then prove tha...

    Text Solution

    |

  15. In triangle ABC, D is the mid point of side BC. If AD is perpendicular...

    Text Solution

    |

  16. Perpendicular drawn from the vertices A,B,C upon opposite sides of tri...

    Text Solution

    |

  17. In triangle ABC if cotA +cot B +cot C=sqrt(3(cotAcotB+cotBcotC+cotAcot...

    Text Solution

    |

  18. The sides of a triangle are in A.P. and the greatest angle exceeds the...

    Text Solution

    |

  19. The sides of a triangle are three consecutive natural numbers and its ...

    Text Solution

    |

  20. If S ,O and G represents circumcentre orthocentre and centroid respect...

    Text Solution

    |