Home
Class 11
MATHS
A B C is a triangle. D is the mid point ...

`A B C` is a triangle. `D` is the mid point of `B Cdot` If `A D` is perpendicular to `A C ,` then prove that `cos A\ dotcos C=(2(c^2-a^2))/(3a c)` .

Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ALLEN|Exercise All Questions|1 Videos

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise Do yourself -6|4 Videos

Similar Questions

Explore conceptually related problems

A B C is a triangle and D is the mid-point of B C . The perpendiculars from D to A B and A C are equal. Prove that the triangle is isosceles.

A B C is a triangle and D is the mid-point of B C . The perpendiculars from D to A B and A C are equal. Prove that the triangle is isosceles.

In any Delta A B C , prove that: a(b\ cos C-c cosB)=b^2-c^2

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A D . Prove that area of B E D = 1/4 area of ABC.

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

In any Delta A B C , prove that: (cos A)/a+(cos B)/b+(cos C)/c=(a^2+b^2+c^2)/(2a b c)

In an isosceles triangle A B C with A B=A C , B D is perpendicular from B to the side A C . Prove that B D^2-C D^2=2\ C D A D

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot

ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions
  1. Prove that : (a b c)/scosA/2cosB/2cosC/2=

    Text Solution

    |

  2. In a DeltaABC, if B=3C, prove that (i) cosC=sqrt(((b+c)/(4c)))" (i...

    Text Solution

    |

  3. A B C is a triangle. D is the mid point of B Cdot If A D is perpendicu...

    Text Solution

    |

  4. Let 1 lt m lt 3. ln a Delta ABC, if 2b= (m+1) a and cos A=1/2 sqrt(((m...

    Text Solution

    |

  5. Prove that : 1/(r1)+1/(r2)+1/(r3)=1/r

    Text Solution

    |

  6. Prove that r1+r2+r3-r=4R

    Text Solution

    |

  7. If r(1), r(2) ,r(3) are the ex-radii of DeltaABC, then prove that (b...

    Text Solution

    |

  8. Consider a D E F , the pedal triangle of the A B C such that A-F-B\ ...

    Text Solution

    |

  9. D E F is the triangle formed by joining the points of contact of the i...

    Text Solution

    |

  10. If sides a , b , c of the triangle A B C are in AdotPdot , then prove ...

    Text Solution

    |

  11. sin6x=sin4x−sin2x then Find the value of x.

    Text Solution

    |

  12. In a Delta ABC, GA,GB,GC makes angles alpha, beta, gamma with each oth...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. If A,A1,A2 and A3 be respectively the areas of the inscribed and escri...

    Text Solution

    |

  15. The value of 1+cot ^2A is

    Text Solution

    |

  16. In a triangle, if the angles A , B ,a n dC are in A.P. show that 2cos1...

    Text Solution

    |

  17. Find BC, if the area of the triangle ABC is <img class="eeimg tr...

    Text Solution

    |

  18. The area of a circle is A 1 and the area of a regular pentagon inscri...

    Text Solution

    |

  19. Let a, b, c be the sides of a triangle . No two of them are equal and ...

    Text Solution

    |

  20. If in a triangle of base 'a', the ratio of the other two sides is r ( ...

    Text Solution

    |