Home
Class 12
MATHS
Consider the following statements concer...

Consider the following statements concerning a `DeltaABC`
(i) The sides a,b,c and area of triangle are rational.
(ii) `a, "tan"(B)/(2),"tan"(C)/(2)`
(iii) `a, sin A sin B, sin C` are rational .
Prove that `(i) rArr(ii) rArr(iii)rArr(i)`

Text Solution

Verified by Experts

The correct Answer is:
Hence `(iii)=>(i).`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise SOLVED EXAMPLES|1 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Sesssion 1|20 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|51 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

If in DeltaABC, A =90^(@) and c, sin B and cos B are rational number, then

For triangle ABC, show that : (i) "sin" (A + B)/(2) = "cos" (C)/(2) (ii) "tan" (B + C)/(2) = "cot" (A)/(2)

If in a DeltaABC, sin A, sin B, sin C are in A.P., show that 3 tan, A/2 tan, C/2 = 1

In DeltaABC, if sin^2 A+ sin^2 B = sin^2 C , then the triangle is

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

In any triangle A B C , prove that: ("sin"(B-C))/("sin"(B+C))=(b^2-c^2)/(a^2)

In any triangle ABC, if sin A , sin B, sin C are in AP, then the maximum value of tan ""B/2 is

If A ,\ B ,\ C are the interior angles of a triangle A B C , prove that tan((C+A)/2)=cotB/2 (ii) sin((B+C)/2)=cosA/2

In any triangle A B C , prove that following: \ a(sin B-sin C)+b( sin C- sin A)+c(sin A-sin B)=0

Statement I In any triangle ABC a cos A+b cos B+c cos C le s. Statement II In any triangle ABC sin ((A)/(2))sin ((B)/(2))sin ((C)/(2))le 1/8

ARIHANT MATHS ENGLISH-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider the following statements concerning a DeltaABC (i) The sid...

    Text Solution

    |

  2. In a triangle XYZ, let x, y, z be the lengths of sides opposite to the...

    Text Solution

    |

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

    Text Solution

    |

  4. Consider a triangle A B C and let a , ba n dc denote the lengths of th...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. Let PQR be a triangle of area Delta with a = 2, b = 7//2, and c = 5//2...

    Text Solution

    |

  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |

  8. Let A B C be a triangle such that /A C B=pi/6 and let a , b and c deno...

    Text Solution

    |

  9. A triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  11. A straight line through the vertex P of a triangle P Q R intersects th...

    Text Solution

    |

  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  16. One angle of an isosceles triangle is 120^0 and the radius of its incr...

    Text Solution

    |

  17. In Delta ABC, which one is true among the following ?

    Text Solution

    |

  18. Let a vertical tower A B have its end A on the level ground. Let C be ...

    Text Solution

    |

  19. ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If...

    Text Solution

    |

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

    Text Solution

    |

  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |