Home
Class 12
MATHS
If sides of triangle ABC are a, b, and c...

If sides of triangle ABC are a, b, and c such that `2b = a + c`, then

A

`(b)/(c) gt (2)/(3)`

B

`(b)/(c) gt (1)/(3)`

C

`(b)/(c) lt 2`

D

`(b)/(c) lt (3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`a + b gt c or 2b - c + b ge c or 3b gt 2c`
or `(b)/(c) gt (2)/(3)`
Also, `b+c gt a or b + c gt 2b - c or 2c gt b`
or `(b)/(c) gt 2`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Comprehension)|34 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Single)|80 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|32 Videos

Similar Questions

Explore conceptually related problems

In a triangle ABC, the side a,b,c are such that they are the roots of then (cosA)/a+(cosB)/b+(cosC)/c=

If the sides of a triangle ABC vary slightly in such a way that 'R' (circum radius) is constant then delta a sec A+delta b .sec B+delta c*sec C=

If the angles A,B, and C of a triangle ABC are in AP and the sides a,b and c opposite to these angles are in GP,then a^(2),b^(2) and c^(2) a are related as

If a, b, c are sides of the triangle ABC and |(1,a, b),(1,c,a),(1,b,c)|=0 , then the value of cos 2A+cos 2B+cos 2C is equal to

If a,b and c are the lengths of the sides of a right triangle ABC with c=2a and b^(2)-3a^(2)=0 , then angleABC=……………………

The sides of triangle ABC satisfy the relations a + b - c= 2 and 2ab -c^(2) =4 , then the square of the area of triangle is ______

Sides of triangle ABC are in A.P.if a

If a, b, c are the sides of a triangle ABC and |(1,a,b),(1,c,a),(1,b,c)|=0, then the value of cos^2 A + cos^2 B +cos^2 C is equal to

CENGAGE-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercise (Multiple)
  1. The sides of DeltaABC satisfy the equation 2a^(2) + 4b^(2) + c^(2) = 4...

    Text Solution

    |

  2. If sides of triangle ABC are a, b, and c such that 2b = a + c, then

    Text Solution

    |

  3. If the sines of the angle A and B of a triangle ABC satisfy the equati...

    Text Solution

    |

  4. There exists triangle ABC satisfying

    Text Solution

    |

  5. In triangle, ABC if 2a^(2) b^(2) + 2b^(2) c^(2) = a^(4) + b^(4) + c^(4...

    Text Solution

    |

  6. If in triangle ABC, a, c and angle A are given and c sin A lt a lt c, ...

    Text Solution

    |

  7. If area of DeltaABC (Delta) and angle C are given and if c opposite to...

    Text Solution

    |

  8. If Delta represents the area of acute angled triangle ABC sqrt(a^(2)b^...

    Text Solution

    |

  9. Sides of DeltaABC are in A.P. If a lt "min" {b,c}, then cos A may be e...

    Text Solution

    |

  10. If the angles of a triangle are 30^(@) and 45^(@), and the included si...

    Text Solution

    |

  11. Lengths of the tangents from A,B and C to the incircle are in A.P., th...

    Text Solution

    |

  12. CF is the internal bisector of angle C of angle ABC, then CF is equal ...

    Text Solution

    |

  13. The incircle of DeltaABC touches side BC at D. The difference between ...

    Text Solution

    |

  14. A circle of radius 4 cm is inscribed in DeltaABC, which touches side B...

    Text Solution

    |

  15. If H is the orthocentre of triangle ABC, R = circumradius and P = AH +...

    Text Solution

    |

  16. Let ABC be an isosceles triangle with base BC. If r is the radius of t...

    Text Solution

    |

  17. If inside a big circle exactly n(nlt=3) small circles, each of radius ...

    Text Solution

    |

  18. The area of a regular polygon of n sides is (where r is inradius, R is...

    Text Solution

    |

  19. In acute angled triangle A B C ,A D is the altitude. Circle drawn with...

    Text Solution

    |

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

    Text Solution

    |