Home
Class 12
MATHS
D is midpoint of BC in Delta ABC such th...

D is midpoint of BC in `Delta ABC` such that AD and AC are perpendicular, Show that `Cos A Cos C = (2 (c^2-a^2))/(3ac)`

Text Solution

Verified by Experts

The correct Answer is:
From Eqs. (i) and(ii) ,`cos A. cos C=(2 (c^(2) -a^(2))/(3ac))`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 2|19 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

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

Similar Questions

Explore conceptually related problems

D is a point on side BC of Delta ABC such that AD=AC (see Fig.7.47). Show that AB>AD

D is a point on side BC of triangle ABC such that AD = AC (see figure). Show that AB gt AD .

D is a point on side BC of Delta ABC such that AD=AC. Show that AB>AD

If D is a point of the base BC an isosceles triangle ABC such that AD is perpendicular to AC, then a=

ABC is triangle. D is the middle point of BC. If AD is perendicular to AC, then prove that cosAcosC=(2(c^(2)-a^(2)))/(3ac)

In Delta ABC, AD and BE are perpendiculars from A and B to the sides BC and AC, then

If D id the mid-point of the side BC of a triangle ABC and AD is perpendicular to AC , then

If D is the mid-point of the side BC of triangle ABC and AD is perpendicular to AC, then 3b^(2)=a^(2)-c( b )3a^(2)=b^(2)3c^(2)b^(2)=a^(2)-c^(2)(d)a^(2)+b^(2)=5c^(2)

In triangle ABC,D is the midpoint of BC and AD is perpendicular to AC. Then cos A.cos C=

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. D is midpoint of BC in Delta ABC such that AD and AC are perpendicular...

    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. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

    Text Solution

    |

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

    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 , ba n dc 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 PQR intersects the ...

    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. Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...

    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 | CD. If ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |