Home
Class 12
MATHS
If R denotes circum-radius of Delta ABC,...

If R denotes circum-radius of `Delta ABC, ` evaluate `(b^(2)-c^(2))/(2aR).`

A

cos (B-C)

B

cos B-cosC

C

sin (B - C)

D

none of these

Text Solution

Verified by Experts

Using `a/(2sinA)=b/(2sinB)=c/(2sinC)=R` we get `(b^(2)-c^(2))/(2aR)=(4R^(2)(sin^(2)B-sin^(2)C))/(4R^(2)sinA)=(sin(B+C)sin(B-C))/(sinA)=sin(B-C)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|95 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise SOLVED MCQ|2 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|31 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

If R denotes circumradius, then in DeltaABC,(b^2-c^2)/(2aR) is equal to

In Delta ABC, a=5, b=4, c=3. G is the centroid of triangle. If R_(1) be the circum radius of triangle GAB then the value of (a)/(65) R_(1)^(2) must be

If Delta denotes the area of DeltaABC , then b^(2) sin 2C + c^(2) sin 2B is equal to

If a, b, c are the sides of Delta ABC such that 3^(2a^(2))-2*3^(a^(2)+b^(2)+c^(2))+3^(2b^(2)+2c^(2))=0 , then Triangle ABC is

If R be circum-radius of a Delta, then circum-radius of a pedal Delta is

Find the value of tan A, if area of Delta ABC is a^(2) -(b-c)^(2).

In Delta ABC , If b/(c^2-a^2)+a/(c^2-b^2)=0 then

The angle of elevation of the top of the tower observed from each of three points A,B , C on the ground, forming a triangle is the same angle alpha. If R is the circum-radius of the triangle ABC, then find the height of the tower

If R be the circum radius and r the in radius of a triangle ABC, show that Rge2r

In a "Delta"A B C , let a ,b , and c denote the length of sides opposite to vertices A, B, and C respectively. If b=2,c=sqrt(3) and /_B A C=pi/6, then value of circumradius of triangle ABC is- 1/2 (2) 1 (3) 2 (4) 1/4

OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
  1. If R denotes circum-radius of Delta ABC, evaluate (b^(2)-c^(2))/(2aR)...

    Text Solution

    |

  2. If the sides of a triangle are in the ratio 3 : 7 : 8, then find R : r

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. In a DeltaABC, angleB=(pi)/(3) and angleC=(pi)/(4) let D divide BC in...

    Text Solution

    |

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

    Text Solution

    |

  7. If in a triangle ABC, right angled at B, s-a=3, s-c=2, then the values...

    Text Solution

    |

  8. If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)), then...

    Text Solution

    |

  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

    Text Solution

    |

  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

    Text Solution

    |

  11. In a DeltaABC, AD is the altitude from A. Given b gt c, angleC=23^(@)"...

    Text Solution

    |

  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

    Text Solution

    |

  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

    Text Solution

    |

  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

    Text Solution

    |

  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

    Text Solution

    |

  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

    Text Solution

    |

  17. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

    Text Solution

    |

  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

    Text Solution

    |

  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

    Text Solution

    |

  20. If in DeltaABC, a=2b and A=3B, then A is equal to

    Text Solution

    |

  21. Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b ...

    Text Solution

    |