Home
Class 12
MATHS
In a triangle ABC if angle ABC=60^(@), t...

In a triangle ABC if `angle ABC=60^(@)`, then `((AB-BC+CA)/(r ))^(2)=`

A

10

B

11

C

12

D

14

Text Solution

Verified by Experts

The correct Answer is:
C
`r=(s-a)tan((A)/(2))`
`therefore r=((AB+BC+CA)/(2)-BC)(1)/(sqrt(3))`
`tehrefore r=(1)/(sqrt(3))(AB-BC+CA)/(2)`
`therefore 2sqrt(3)=(AB-BC+CA)/(r )`
`therefore ((AB-BC+CA)/(r ))^(2)=12`
Promotional Banner

Topper's Solved these Questions

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE|Exercise Comprehension Type|6 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|3 Videos

  • STATISTICS

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

Construct a triangle ABC, in which angleB =60^(@),angleC=45^(@) and AB + BC + CA = 11 cm.

In a triangle ABC , if angle A=60 , a=5,b=4 then c is a root of the equation

Solve the triangle ABC if a=5 , b=4 and angle A =60^(@ , then side c is

Can you construct a triangle ABC with BC = 6 cm, angleB=60^(@) and AB + AC = 5cm.? If not, give reasons.

In a triangle ABC, angle A = 30^(@), BC = 2 + sqrt5 , then find the distance of the vertex A from the orthocenter

Draw a triangle ABC of base BC=8 cm, angle A=60^(@) and the bisector of angle A meets BC at D such that BD=6 cm.

In a triangle ABC , (c^2 +a^2 -b^2)/(2ca) is:

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL^(2)+ CM^(2))=5BC^(2)

Find the angle A in triangle ABC, if angle B=60^∘ and angle c=70^∘

Draw a triangle ABC of base BC=8 cm, angleA=60^(@) and the bisector of angle A meets BC at D such that BD=6 cm .

CENGAGE-SOLUTIONS AND PROPERTIES OF TRIANGLE -SINGLE CORRECT ANSWER TYPE
  1. Let ABC be an equilateral triangle, let KLMN be a rectangle with K...

    Text Solution

    |

  2. ABC is an acute angled triangle with circumcenter O and orthocentre H....

    Text Solution

    |

  3. In a triangle ABC if angle ABC=60^(@), then ((AB-BC+CA)/(r ))^(2)=

    Text Solution

    |

  4. The area of an acute triangle ABC is Delta, the area of its pedal tria...

    Text Solution

    |

  5. In a triangle ABC, D is a point on BC such that AD is the internal bis...

    Text Solution

    |

  6. In Delta ABC, circumrdius is 3 inradius is 1.5 units. The value of a a...

    Text Solution

    |

  7. AD, BE, CF are internal angular bisectors of Delta ABC and I is the in...

    Text Solution

    |

  8. In Delta ABC it is given distance between the circumcentre (O) and ort...

    Text Solution

    |

  9. In any Delta ABC line joiningcircumcentre (O) and incentre (I) is para...

    Text Solution

    |

  10. Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and...

    Text Solution

    |

  11. Let H be the orthocentre of triangle ABC. Then angle subtended by side...

    Text Solution

    |

  12. If in a triangle ABC, r(1)+r(2)+r(3)=9r, then the triangle is necessar...

    Text Solution

    |

  13. In triangle ABC, r=(R )/(6) and r(1)=7r. Then the measure of angle A =

    Text Solution

    |

  14. (r(2)+r(3))sqrt((r r(2))/(r(2)r(3)))=

    Text Solution

    |

  15. In Delta ABC, right angled at A, cos^(-1)((R )/(r(2)+r(3))) is

    Text Solution

    |

  16. In Delta ABC if r1=2r2=3r3 and D is the mid point of BC then cos/ADC=

    Text Solution

    |

  17. In the ambiguous case if the remaining angles of a triangle with given...

    Text Solution

    |

  18. Two sides of a triangle are of lengths sqrt6 and 4 and the angle oppos...

    Text Solution

    |

  19. If circumradius of triangle is 2, then the maximum value of (abc)/(a+b...

    Text Solution

    |

  20. Let ABC and AB'C be two non-congruent triangles with sides BC=B'C=5, A...

    Text Solution

    |