Home
Class 12
MATHS
ABC is a triangle. D is the middle point...

ABC is a triangle. D is the middle point of BC. If AD is perpendicular to AC, The value of cos A cos C , is

A

`(3(c^(2)-a^(2))/(ac)`

B

`(a^(2)-c^(2))/(2ac)`

C

`(2(c^(2)-a^(2))/(3ac)`

D

none of these

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( \cos A \cos C \) given that \( D \) is the midpoint of \( BC \) and \( AD \) is perpendicular to \( AC \). ### Step-by-Step Solution: 1. **Draw Triangle ABC**: - Let \( A \), \( B \), and \( C \) be the vertices of the triangle. - Let \( D \) be the midpoint of side \( BC \). ...
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise SOLVED MCQ|2 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 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

In triangle ABC, AB > AC. E is the mid-point of BC and AD is perpendicular to BC. Prove that : AB^2 +AC^2=2AE^2 +2BE^2

In the given figure ABC is a triangle and D is the mid-point of BC. AD is produced to E. BM and CN are two perpendiculars dropped from B and C respectively on AE. Prove that : BM=CN

In the given figure ABC is a triangle and D is the mid-point of BC. AD is produced to E. BM and CN are two perpendiculars dropped from B and C respectively on AE. Prove that : DeltaBMD~=DeltaCND

The given figure shows a triangle ABC, in which AB gt AC . E is the mid-point of BC and AD is perpendicular to BC. Prove that AB^(2)- AC^(2)= 2BCxxED .

The given figure shows a triangle ABC, in which AB gt AC. E is the mid-point of BC and AD is perpendicular to BC. Prove that : AB^(2) +AC^(2) =2BE^2 +2AE^2

In a triangle ABC,D is the mid - point of BC, AD is produced upto E so that DE = AD. Prove that : AB=EC

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

ABC is a right angled triangle with ABC = 90^@ . D is any point on AB and DE is perpendicular to AC. Prove that: If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.

ABC is a right angled triangle with ABC = 90^@ . D is any point on AB and DE is perpendicular to AC. Prove that: DeltaADE~DeltaACB .

In a Delta ABC , the median AD is perpendicular to AC. If b = 5 and c = 11, then a =

OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Section I - Solved Mcqs
  1. If the perimeter of a triangle and the diameter of an ex-circle are eq...

    Text Solution

    |

  2. If D id the mid-point of the side BC of a triangle ABC and AD is perpe...

    Text Solution

    |

  3. ABC is a triangle. D is the middle point of BC. If AD is perpendicular...

    Text Solution

    |

  4. If the median of a triangle through A is perpendicular to AB, then

    Text Solution

    |

  5. In a triangle ABC , if r(1) =2r(2) =3r(3) , then a:b:c =

    Text Solution

    |

  6. In Delta ABC, if r(1) lt r(2) lt r(3), then find the order of lengths ...

    Text Solution

    |

  7. In a triangle ABC if r(1) = 8, r(2) = 12 and r(3) = 24, then a =

    Text Solution

    |

  8. If I is the incentre of a DeltaABC such that angleA=60^(@), then AI =

    Text Solution

    |

  9. If I(1) is the centre of the escribed circle touching side BC of !ABC ...

    Text Solution

    |

  10. In a triangle ABC , if 2R + r = r(1) , then

    Text Solution

    |

  11. The sides of a triangle are sin alpha, cos alpha, sqrt(1+sin alpha cos...

    Text Solution

    |

  12. In a triangle ABC , if 3a = b + c , then cot B/2 cot C/2 =

    Text Solution

    |

  13. If sin^(2).(A)/(2), sin^(2).(B)/(2), and sin^(2).(C)/(2) are in H.P., ...

    Text Solution

    |

  14. In a triangle ABC , if 1/(b+c)+1/(c+a)=3/(a+b+c), then angleC=

    Text Solution

    |

  15. Observe the following statements: (I) In !ABC,bcos^(2)C/2+ccos^(2)B/2=...

    Text Solution

    |

  16. In a triangle , if r(1) = 2r(2) = 3r(3), then a/b + b/c + c/a is equa...

    Text Solution

    |

  17. Sides a , b , c of !ABC are in A.P. and costheta(1)=a/(b+c)costheta(2)...

    Text Solution

    |

  18. Consider a triangle ABC and let a, b and c denote the lengths of the s...

    Text Solution

    |

  19. If the angles A, B and C of a triangle are in an arithmetic progressio...

    Text Solution

    |

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

    Text Solution

    |