Home
Class 12
MATHS
lf in DeltaABC,b^(2)sin 2C + c^(2) sin 2...

lf in `DeltaABC,b^(2)sin 2C + c^(2)` sin 2B = 2bc,then the triangle is

A

equilateral

B

isosceles with `angleB=angleC`

C

right angled at A

D

none of these

Text Solution

Verified by Experts

We have,
`b^(2)sin2C+c^(2)sin2B=2bc`
`rArr4Delta=2bc`(See illustration6)
`rArr(abc)/R=2bc` `[becauseR=(abc)/(4Delta)]`
`rArra=2R`
`rArr2RsinA=2R` `[because a/(sinA)=2R]`
`rArrsinA=1rArrA=(pi)/2`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

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

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA|Exercise SOLVED MCQ|2 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

In Delta ABC,b^(2)sin2C+c^(2)sin2B=

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

In a DeltaABC,R^(2) (sin 2A+sin 2B+sin 2C)=

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

In triangle ABC, b^(2) sin 2C + c^(2) sin 2B = 2bc where b = 20, c = 21 , then inradius =

In any Delta ABC, prove that b^(2)sin2C+c^(2)sin2B=2bc sin A=4Delta

In a Delta ABC if a^(2)sin(B-C)+b^(2)sin(C-A)+c^(2)sin(A-B)=0, then triangle is

In a triangle ABC, if a, b, c are in A.P. and (b)/(c) sin 2C + (c)/(b) sin 2B + (b)/(a) sin 2A + (a)/(b) sin 2B = 2 , then find the value of sin B

In triangle ABC,b^(2)sin2C+c^(2)sin2B=2bc where b=20,c=21 then inradius =4 (b) 6(c)8(d)9

In any DeltaABC, sum a^(2) (sin^2 B - sin^2 C) =

OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
  1. lf in DeltaABC,b^(2)sin 2C + c^(2) sin 2B = 2bc,then the triangle is

    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 the reactangle polygen of n sides is (where R is the radiu...

    Text Solution

    |

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

    Text Solution

    |

  5. In a triagnle ABC, angle B=pi/3 " and " angle C = pi/4 let D divide ...

    Text Solution

    |

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

    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 bgtc ,angleC=23^(@) an...

    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 a DeltaABC, A=(2pi)/3, b-c=3sqrt3 cm and area(DeltaABC)=(9sqrt3)/2 ...

    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 , B and C of triangle A B C be in AdotPdot and let b ...

    Text Solution

    |