Home
Class 11
MATHS
If sides of triangle A B C are a , ba n ...

If sides of triangle `A B C` are `a , ba n dc` such that `2b=a+c` then `b/c >2/3` (b) `b/c >1/3` `b/c<2` (d) `b/c<3/2`

Text Solution

Verified by Experts

`a+b>c`
`2b-c+b>c`
`3b-c>c`
`3b>2c`
`b/c>2/3`
Option C is correct.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|381 Videos

Similar Questions

Explore conceptually related problems

If the sides of a Delta ABC are a = 4, b = 6 and c = 8, show that 4 cos B + 3 cos C = 2.

If an a triangle A B C , b=3ca n d C-B=90^0, then find the value of tanB

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then (a) 3b^2=a^2-c (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

If the sides of Delta ABC are a = 4, b = 6 , c = 8 , then show that 4 cos B + 3 cos C = 2.

If in a triangle A B C ,/_C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+b+c) .

a triangle A B C with fixed base B C , the vertex A moves such that cosB+cosC=4sin^2(A/2)dot If a ,ba n dc , denote the length of the sides of the triangle opposite to the angles A , B ,a n dC , respectively, then (a) b+c=4a (b) b+c=2a (c) the locus of point A is an ellipse (d) the locus of point A is a pair of straight lines

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , 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

Let D be the middle point of the side B C of a triangle A B Cdot If the triangle A D C is equilateral, then a^2: b^2: c^2 is equal to 1:4:3 (b) 4:1:3 (c) 4:3:1 (d) 3:4:1

If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 , where a , ba n dc are the sides of a triangle ABC, then cosB is equal to 1-c/(2a) (b) 1-c/a 1+c/(c a) (d) 1+c/(3a)

A plane makes intercepts O A ,O Ba n dO C whose measurements are a,b and c on the O X ,O Ya n dO Z axes. The area of triangle A B C is a. 1/2(a b+b c+c a) b. 1/2a b c(a+b+c) c. 1/2(a^2b^2+b^2c^2+c^2a^2)^(1//2) d. 1/2(a+b+c)^2

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. If angle C of triangle ABC is 90^0, then prove that tanA+tanB=(c^2)/(a...

    Text Solution

    |

  2. The sides of A B C satisfy the equation 2a^2+4b^2+c^2=4a b+2a cdot Th...

    Text Solution

    |

  3. If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >...

    Text Solution

    |

  4. By geometrical interpretation, prove that (i) sin(alpha+beta)=si...

    Text Solution

    |

  5. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2theta........

    Text Solution

    |

  6. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a1+x)++1/(2^(n-1))cos(an+x)...

    Text Solution

    |

  7. Three circles touch each other externally. The tangents at their point...

    Text Solution

    |

  8. Prove that tan20^0tan40^0tan60^0tan80^0=3

    Text Solution

    |

  9. If cottheta+tantheta=x and sectheta-costheta=y , prove that (x^2y)^(...

    Text Solution

    |

  10. The solution of the system of equations sinxsiny=(sqrt(3))/4,cosxcosy=...

    Text Solution

    |

  11. Find the least value of sec A+secB+secC in an acute angled triangle

    Text Solution

    |

  12. If in triangle A B ,cosAcosB+sinAsinBsinC=1. Show that a : b : c=1:1:s...

    Text Solution

    |

  13. Let f(x) = sin^6x + cos^6x + k(sin^4 x + cos^4 x) for some real numbe...

    Text Solution

    |

  14. Number of integral values of a for which the equation cos^2x-sinx+a=0 ...

    Text Solution

    |

  15. In A B C , prove that cosA+cosB+cosClt=3/2dot

    Text Solution

    |

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

    Text Solution

    |

  17. If pcos e ctheta+qcottheta=2 and p^2cos e c^2theta-q^2cot^2theta=5 t...

    Text Solution

    |

  18. In a /\A B C , if tanA/2,tanB/2,tanC/2"are in"AdotPdot, then show t...

    Text Solution

    |

  19. With usual notion, if in triangle A B C , (b+c)/(11)=(c+a)/(12)=(a+b)...

    Text Solution

    |

  20. Solution of the equation sin(sqrt(1+sin2theta))=sintheta+costhetai s(n...

    Text Solution

    |