Home
Class 12
MATHS
In a DeltaABC, r(1) + r(2) + r(3) -r=...

In a `DeltaABC, r_(1) + r_(2) + r_(3) -r`=

A

4R cos A

B

4R cos B

C

4R cos C

D

4R

Text Solution

Verified by Experts

We have,
`r_(1)+r_(2)+r_(3)-r`
`=4R{sinA/2cosB/2cosC/2+sinB/2cosC/2cosA/2+sinC/2cosA/2cosB/2-sinA/2sinB/2sinC/2}`
`=4R{cosC/2sin((A+B)/2)+sinC/2cos((A+B)/2)}`
`=4Rsin((A+B)/2+C/2)=4R[because a+B+C=pi]`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|95 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise SOLVED MCQ|2 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

In DeltaABC, R, r, r_(1), r_(2), r_(3) denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that r_(1) :r_(2): r_(3) = 1: 2 : 3 The value of R : r is

In DeltaABC, R, r, r_(1), r_(2), r_(3) denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that r_(1) :r_(2): r_(3) = 1: 2 : 3 The sides of the triangle are in the ratio

In DeltaABC, R, r, r_(1), r_(2), r_(3) denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that r_(1) :r_(2): r_(3) = 1: 2 : 3 The greatest angle of the triangle is given by

In a DeltaABC, if r_(1)=2r _(2)=3r_(3), then show that a/b=5/4.

If a right angled DeltaABC of maximum area is inscribled within a circle of radius R, then (delta representes area of DeltaABCand r, r_(1), r_(2), r_(3) represent in-radius and ex-radii, and s is the semi-perimeter of DeltaABC, then

In a DeltaABC, show that r_(1)* r_(2)* r_(3)*r=Delta^(2).

In any Delta ABC,r_(1),r_(2),r_(3),r stands for its usual meaning then (1)/(r_(1))+(1)/(r_(2))+(1)/(r_(3)) is

If r_(1),r_(2),r_(3),r are in usual notation in Delta ABC then r_(1)r_(2)r_(3)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))=

OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
  1. In a DeltaABC, r(1) + r(2) + r(3) -r=

    Text Solution

    |

  2. If the sides of a triangle are in the ratio 3 : 7 : 8, then find R : r

    Text Solution

    |

  3. The area of the reactangle polygen of n sides is (where R is the radiu...

    Text Solution

    |

  4. If the angles of a rectangle are 30^(@) and 45^(@) and the included si...

    Text Solution

    |

  5. In a triagnle ABC, angle B=pi/3 " and " angle C = pi/4 let D divide ...

    Text Solution

    |

  6. If A is the area and 2s the sum of the sides of a triangle,then

    Text Solution

    |

  7. If in a triangle ABC, right angled at B, s-a=3, s-c=2, then the values...

    Text Solution

    |

  8. If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)), then...

    Text Solution

    |

  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

    Text Solution

    |

  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

    Text Solution

    |

  11. In a DeltaABC, AD is the altitude from A. Given bgtc ,angleC=23^(@) an...

    Text Solution

    |

  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

    Text Solution

    |

  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

    Text Solution

    |

  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

    Text Solution

    |

  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

    Text Solution

    |

  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

    Text Solution

    |

  17. In a DeltaABC, A=(2pi)/3, b-c=3sqrt3 cm and area(DeltaABC)=(9sqrt3)/2 ...

    Text Solution

    |

  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

    Text Solution

    |

  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

    Text Solution

    |

  20. If in DeltaABC, a=2b and A=3B, then A is equal to

    Text Solution

    |

  21. Let the angles A , B and C of triangle A B C be in AdotPdot and let b ...

    Text Solution

    |