Home
Class 12
MATHS
If in a !ABC ,a^(2)+b^(2)+c^(2)=ac+sqrt3...

If in a `!ABC` ,`a^(2)+b^(2)+c^(2)=ac+sqrt3ab` then the triangle is

A

equilateral

B

right angled and isosceles

C

right angled and not isosceles

D

none of these

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the given equation in the triangle \( ABC \): Given: \[ a^2 + b^2 + c^2 = ac + \sqrt{3}ab \] ### Step 1: Rearranging the equation ...
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise SOLVED MCQ|2 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 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

If in a triangle ABC,a^(2)+b^(2)+c^(2)=ca+ab sqrt(3) then the triangle is

If in a triangle ABC,a^(2)+b^(2)+c^(2)=ca+ab sqrt(3), then the triangle is

If in triangle ABC,a^(2)+b^(2)+c^(2)-ac-sqrt(3)ab=0 ,then triangle is necessarily. 1) isosceles 2) right angled 3) obtuse angled 4) equilateral

In triangleABC , if a^(2)+b^(2)+c^(2)=ac+ab sqrt(3) , then

If sin A and sin B of a triangle ABC satisfy c^(2)x^(2)-c(a+b)x+ab=0, then the triangle is

If, in a Delta ABC, c^(2) + a^(2) - b^(2) = ac , then : /_B =

In Delta ABC2a^(2)+4b^(2)+c^(2)=2ab+2ac then numerical value of cos B is

In a triangle ABC, if sin A sin B= (ab)/(c^(2)) , then the triangle is :

In Delta ABC , if AB^(2) = AC^(2) + CB^(2) . State with reason whether Delta ABC is a right angled triangle or not.

triangleABC is an isosceles triangle with AC = BC. If AB^(2)= 2AC^(2) . Prove that triangle ABC is a right triangle.

OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
  1. In any !ABC , sin A/2 is

    Text Solution

    |

  2. In a !ABC , AB = 2, BC =4 ,CA = 3. If D is the mid-point of BC, then t...

    Text Solution

    |

  3. If in a !ABC ,a^(2)+b^(2)+c^(2)=ac+sqrt3ab then the triangle is

    Text Solution

    |

  4. In a !ABC bisector of angle C meets the side AB at D and circumcricle ...

    Text Solution

    |

  5. In triangle ABC, AD and BE are the medians drawn through the angular ...

    Text Solution

    |

  6. If the median AM , angle bisector AD and altitude AH drawn from vertex...

    Text Solution

    |

  7. Which of the following pieces of data does not uniquely determine an a...

    Text Solution

    |

  8. If a chord AB of a circle subtends an angle theta(nepi//3) at a point ...

    Text Solution

    |

  9. In a !ABC , medians AD and BE are drawn. If AD = 4, angleDAB=pi//6 and...

    Text Solution

    |

  10. In a !ABC if sin A cos B = 1/4 and 3 tan A = B , then the triangle is

    Text Solution

    |

  11. In a !ABC if r(1) = 36 , r(2) = 18 and r(3) = 12, then the area of the...

    Text Solution

    |

  12. In a !ABC if r(1) = 36 , r(2) = 18 and r(3) = 12 , then the perimeter ...

    Text Solution

    |

  13. If in a Delta ABC, AD, BE and CF are the altitudes and R is the circum...

    Text Solution

    |

  14. In a !ABC if a = 7 , b = 8 and c = 9 , then the length of the line joi...

    Text Solution

    |

  15. If the perimeter of a triangle and the diameter of an ex-circle are eq...

    Text Solution

    |

  16. If D id the mid-point of the side BC of a triangle ABC and AD is perpe...

    Text Solution

    |

  17. ABC is a triangle. D is the middle point of BC. If AD is perpendicular...

    Text Solution

    |

  18. If the median of a triangle through A is perpendicular to AB, then

    Text Solution

    |

  19. In a !ABC , if r(1) =2r(2) =3r(3) , then a:b:c =

    Text Solution

    |

  20. In a !ABC if r(1)ltr(2)ltr(3), then

    Text Solution

    |