Home
Class 12
MATHS
In a !ABC , if 3a = b + c , then cot B/2...

In a `!ABC` , if 3a = b + c , then cot `B/2` cot `C/2` =

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

We have,
`3a=b+crArr4a=a+b+crArr4a=2srArrs=2a`
`thereforecotB/2cotC/2=sqrt((s(s-b))/((s-a)(s-c)))sqrt((s(s-c))/((s-a)(s-b)))`
`rArrcotB/2cotC/2=s/(s-a)=(2a)/(2a-a)=2`
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 Delta ABC, 3a = b + c then: cot (B/2) cdot cot (C/2) = .....

In /_ABC, if 3a=b+c, then cot((B)/(2))cot((C)/(2))=

In a hat grad ABC if b+c=3a, then cot (B)/(2). cot (C)/(2) has the value equal to: 4 b.3 c.2d.1

In Delta ABC , if a = 10 and b cot B + c cot C = 2(r + R) then the maximum area of DeltaABC will be

In a /_ABC, if b^(2)+c^(2)=3a^(2), then cot B+cot C-cot A is equal to

In any Delta ABC , If cot ""A/2 , cot ""B/2 ,cot ""C/2 are in AP, then a,b,c are in

If in a triangle ABC ,b +c=4a then cot(B/2)cot(C/2) is equal to

In /_\ ABC, if 2b=a+c then cot(A/2)cot(C/2)=

If in a ABC,tan A+tan B+tan C=0 then cot A cot B cot C=6b.1c*(1)/(6)d .none of these

If, in a Delta ABC, b^(2) + c^(2) = 3a^(2) , then : cot B + cot C - cot A =

OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
  1. In a !ABC , if 2R + r = r(1) , then

    Text Solution

    |

  2. The sides of the triangle are sinalpha , cosalpha and sqrt(1+sinalphac...

    Text Solution

    |

  3. In a !ABC , if 3a = b + c , then cot B/2 cot C/2 =

    Text Solution

    |

  4. In !ABC , if sin^(2)A/2,sin^(2)B/2,sin^(2)C/2 be in H.P., then a , b ,...

    Text Solution

    |

  5. In a !ABC , if 1/(b+c)+1/(c+a)=3/(a+b+c), then angleC=

    Text Solution

    |

  6. Observe the following statements: (I) In !ABC,bcos^(2)C/2+ccos^(2)B/2=...

    Text Solution

    |

  7. In a triangle , if r(1) = 2r(2) = 3r(3), then a/b + b/c + c/a is equa...

    Text Solution

    |

  8. Sides a , b , c of !ABC are in A.P. and costheta(1)=a/(b+c)costheta(2)...

    Text Solution

    |

  9. Consider a triangle ABC and let a , b , and c denote the lengths of t...

    Text Solution

    |

  10. If the angle A , B and C of a triangle are in arithmetic progession an...

    Text Solution

    |

  11. Let ABC be a triangle such that angleACB=pi/6 and let a , b and c deno...

    Text Solution

    |

  12. For a regular polygon , let r and R be the radii of the inscribed and ...

    Text Solution

    |

  13. Let PQR be a triangle of ! area with a = 2 , b = 7/2 and c = 5/2, wher...

    Text Solution

    |

  14. ABCD is a trapezium such that AB and CD are parallel and BCbotCD. if a...

    Text Solution

    |

  15. In a triangle PQR ,P is the largest angle and cos P = 1/3 . further th...

    Text Solution

    |

  16. In a triangle the sum of two sides is x and the product of the same tw...

    Text Solution

    |

  17. In !ABC , if (sinA)/(csinB)+(sinB)/c+sinC)/b=c/(ab)+b/(ac)+a/(bc) the...

    Text Solution

    |

  18. In !ABC , if 2b = a + c and A - C =90^(@) , then sin B equals

    Text Solution

    |

  19. In a !XYZ ,let x , y , z be the length of the side opposite to angles....

    Text Solution

    |

  20. If s−x/4= s−y/3=s-z/2 and area of incircle of the triangle XYZ is ...

    Text Solution

    |