Home
Class 11
MATHS
Prove that r1+r2+r3-r=4R...

Prove that `r_1+r_2+r_3-r=4R`

Promotional Banner

Topper's Solved these Questions

  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise EXERCISE (S-1)|44 Videos

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise Do yourself -6|4 Videos

Similar Questions

Explore conceptually related problems

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

If I is the incenter of Delta ABC and R_(1), R_(2), and R_(3) are, respectively, the radii of the circumcircle of the triangle IBC, ICA, and IAB, then prove that R_(1) R_(2) R_(3) = 2r R^(2)

In any Delta ABC, prove that r.r_(1).r_(2).r_(3)=Delta^(2)

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)

Prove that : (r_1-r)/(a) +(r_2-r)/(b) = (c )/(r_3) .

Prove that : (r_1+r_2) tan (C )/(2) = (r_3- r) cot ( C)/(2) = c

" (i) Show that "r+r_(1)+r_(2)-r_(3)=4R cos C

In any A B C , prove that r^2+r1 2+r2 2+r3 2=16 R^2-a^2-b^2-c^2dot

In a triangle ABC, prove that r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2.

ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions
  1. For any triangle ABC, If B=3C, show that cosC=sqrt((b+c)/(4c)) and s...

    Text Solution

    |

  2. A B C is a triangle. D is the mid point of B Cdot If A D is perpendicu...

    Text Solution

    |

  3. Prove that r1+r2+r3-r=4R

    Text Solution

    |

  4. In a Delta ABC, GA,GB,GC makes angles alpha, beta, gamma with each oth...

    Text Solution

    |

  5. In a DeltaABC, the median to the side BC is of length 1/sqrt(11-6sqrt...

    Text Solution

    |

  6. Prove that : (r1)/(b c)+(r2)/(c a)+(r3)/(a b)=1/r-1/(2R)

    Text Solution

    |

  7. Prove that : (tanA/2)/((a-b)(a-c))+(tanB/2)/((b-a)(b-c))+(tanC/2)/((c-...

    Text Solution

    |

  8. Prove that in a triangle (b c)/(r1)+(c a)/(r2)+(a b)/(r3)=2R\ [(a/b+b...

    Text Solution

    |

  9. In a triangle, if the angles A , B ,a n dC are in A.P. show that 2cos1...

    Text Solution

    |

  10. In a scalene triangle ABC the altitudes AD & CF are dropped from the v...

    Text Solution

    |

  11. Let a, b, c be the sides of a triangle & Delta its area. Prove that a^...

    Text Solution

    |

  12. If in a triangle of base 'a', the ratio of the other two sides is r ( ...

    Text Solution

    |

  13. If Delta is the area of a triangle with side lengths a, b, c, then s...

    Text Solution

    |

  14. Which of the following pieces of data does NOT uniquely determine an ...

    Text Solution

    |

  15. If a ,b ,c are the sides of a triangle such that a : b : c=1:sqrt(3...

    Text Solution

    |

  16. If a ,b ,c denote the lengths of the sides of a triangle opposite t...

    Text Solution

    |

  17. One angle of an isosceles triangle is 120^0 and the radius of its incr...

    Text Solution

    |

  18. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  19. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  20. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |