Home
Class 12
MATHS
Consider a triangle ABC, where x,y,z are...

Consider a triangle ABC, where x,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters `R,r,S,Delta` denote the circumradius, inradius semi-perimeter and area of the triangle respectively.
The valur of `(c sin B+b sin C)/(x)+ (a sin C +c sin A)/(y)+(b sin A+a sin B)/(z)` is equal to

A

`R/r`

B

`S/R`

C

2

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise PROPERTIES AND SOLUTIONS OF TRIANGLES EXERCISE 5: MATCHING TYPE QUESTIONS|4 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|16 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|15 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

Consider a triangle ABC, where x,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. If cot A+cot B+ cot C= k ((1)/(x^(2))+ (1)/(y^(2))+(1)/(z^(2))), then the value of k is

Consider a triangle ABC, where x,y,z are the length of perpendicular drawn from the vertices of the triangle to the opposite sides a,b, c respectively. Let the letters R,r S,Delta denote the circumradius, inradius semi-perimeter and area of the triangle respectively. If (bx)/(c) +(cy)/(a)+(az)/(b) =(a^(2) +b^(2)+c ^(2))/(k), then the value of k is

In a triangle, sec A (cos B cos C-sin B sin C) is equal to :

In a triangle, cosec A (sin B cos C + cos B sin C) is equal to :

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. Radius is the circum circle of Delta LMN is

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. If perimeters of DeltaLMN and Delta ABC an lamda and mu, then the value of (lamda)/(mu) is

In any triangle ABC, prove that : a sin (B -C) + b sin (C -A) +c sin (A-B) = 0 .

Consider a triangle A B C and let a , b and c denote the lengths of the sides opposite to vertices A , B ,and C , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

Show that Rr (sin A+sin B + sin C) =Delta

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Passage Based Questions)
  1. Let ABC to be an acute triangle with BC=a,CA =b and AB=c, where a ne ...

    Text Solution

    |

  2. In an acute angled triangle ABC, let AD, BE and CF be the perpendicula...

    Text Solution

    |

  3. In an acute angle Delta ABC, let AD, BE and CF be the perpendicular fr...

    Text Solution

    |

  4. In an acute angle Delta ABC, let AD, BE and CF be the perpendicular fr...

    Text Solution

    |

  5. Let a,b, c are the sides opposite to angles A, B , C respectively in a...

    Text Solution

    |

  6. Let a,b, c are the sides opposite to angles A, B , C respectively in a...

    Text Solution

    |

  7. Let a,b, c are the sides opposite to angles A, B , C respectively in a...

    Text Solution

    |

  8. Find dy/dx , if x = 4/t and y = 4t

    Text Solution

    |

  9. If x and y are connected parametrically by the equation , without elim...

    Text Solution

    |

  10. Find dy/dx , if x = a sint , y = a(cost + log (tan (t/2))

    Text Solution

    |

  11. Find dy/dx , if x = cos(theta) and y = sin(2theta)

    Text Solution

    |

  12. Differentiate the following function w.r.t x cos^(-1)x/(2x+7)^(1...

    Text Solution

    |

  13. Consider a triangle ABC, where x,y,z are the length of perpendicular d...

    Text Solution

    |

  14. Consider a triangle ABC, where x,y,z are the length of perpendicular d...

    Text Solution

    |

  15. Consider a triangle ABC, where x,y,z are the length of perpendicular d...

    Text Solution

    |

  16. AL, BM and CN are perpendicular from angular points of a triangle ABC ...

    Text Solution

    |

  17. The angle of triangle A, B, C are in AP and C=3A . Find angle B

    Text Solution

    |

  18. AL, BM and CN are perpendicular from angular points of a triangle ABC ...

    Text Solution

    |

  19. AL, BM and CN are perpendicular from angular points of a triangle ABC ...

    Text Solution

    |

  20. Differentiate the following w.r.t x (2x^2-6x+4)^3

    Text Solution

    |