Home
Class 12
MATHS
If p(1), p(2) and p(3) are the altitu...

If `p_(1), p_(2)` and `p_(3)` are the altitudes of a triangle from the vertices of a `Delta ABC` and `Delta` is the area of triangle, prove that : `(1)/(p_(1)) + (1)/(p_(2)) - (1)/(p_(3)) = (2ab)/((a+b+c)Delta) cos^(2).(C )/(2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|35 Videos

  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos

  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos

  • PROBABILITY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|102 Videos

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advance ( Archive )|20 Videos

Similar Questions

Explore conceptually related problems

If p_(1),p_(2),p_(3) are the altitues of a triangle from the vertieces A,B,C and Delta is the area of the triangle then prove that (1)/(p_(1))+(1)/(p_(2))-(1)/(p_(3))=(2ab)/((a+b+c)Delta)"cos"^(2)(C)/(2)

If P_1, P_2 and P_3 are the altitudes of a triangle from vertices A, B and C respectively and Delta is the area of the triangle, then the value of 1/P_1+1/P_2-1/P_3=

P_(1), P_(2), P_(3) are altitudes of a triangle ABC from the vertices A, B, C and Delta is the area of the triangle, The value of P_(1)^(-1) + P_(2)^(-1) + P_(3)^(-1) is equal to-

If p_(1),p_(2),p_(3) are altitudes of a triangle ABC from the vertices A,B,C and ! the area of the triangle, then p_(1).p_(2),p_(3) is equal to

If p_(1),p_(2),p_(3) are altitudes of a triangle ABC from the vertices A,B,C and triangle the area of the triangle, then p_(1)^(-2)+p_(2)^(-2)+p_(3)^(-2) is equal to

If p_1,p_2,p_3 re the altitudes of the triangle ABC from the vertices A, B and C respectivel. Prove that (cosA)/p_1+(cosB)/p^2+(cosC)/p_3 =1/R

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

A(-3, 1), B(4,4) and C(1, -2) are the vertices of a triangle ABC. Find: the equation of altitude AE.

If alpha, beta and gamma are the lengths of altitudes ABC and Delta be its area prove that : (1)/(alpha^(2))+(1)/(beta^(2)) + (1)/(gamma^(2)) = ((cot A + cot B + cot C))/(Delta)

Find the equation of the altitudes of triangle ABC whose vertices are A(2,-2), B(1,1) and C(-1,0)

VMC MODULES ENGLISH-PROPERTIES OF TRIANGLE-Level - 2
  1. If in a Delta ABC, cot A + cot B + cot C = sqrt(3) . Prove that trian...

    Text Solution

    |

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

    Text Solution

    |

  3. If p(1), p(2) and p(3) are the altitudes of a triangle from the ver...

    Text Solution

    |

  4. If alpha, beta and gamma are the lengths of altitudes ABC and Delt...

    Text Solution

    |

  5. Prove the questions a(r r(1) + r(2)r(3)) = b(r r(2) + r(3) r(1)) = ...

    Text Solution

    |

  6. The value of 1/(r(1)^(2))+1/(r(2)^(2))+1/(r(2)^(3))+1/(r^(2)), is

    Text Solution

    |

  7. In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

    Text Solution

    |

  8. Prove that (r(2) + r(3))/(1 + cos A) = (r(3) + r(1))/(1 + cos B) =...

    Text Solution

    |

  9. If the lengths of the perpendiculars from the vertices of a triangle A...

    Text Solution

    |

  10. Prove that the distance of the incentre of Delta ABC from A is 4R si...

    Text Solution

    |

  11. The sides of a triangle are three consecutive natural numbers and its ...

    Text Solution

    |

  12. If A, A(1), A(2), A(3) are the areas of the inscribed and escribed of ...

    Text Solution

    |

  13. If in a triangle, (1-(r(1))/(r(2))) (1 - (r(1))/(r(3))) = 2, then the ...

    Text Solution

    |

  14. In a triangle Delta ABC, prove the following : 2 abc cos.(A)/(2) co...

    Text Solution

    |

  15. In a triangle Delta ABC, prove the following : (tan A//2)/((a-b)(a-...

    Text Solution

    |

  16. If the angle opf a triangle are in the ratio 1:2:3, then show that the...

    Text Solution

    |

  17. If a cosA=b cos B, then prove that either the triangle is isosceles or...

    Text Solution

    |

  18. If in Delta ABC, c(a+b) cos ""1/2 B=b (a+c) cos ""1/2 C, the triangle ...

    Text Solution

    |

  19. Let A, B be two points on the bank of a straight river, and C, D point...

    Text Solution

    |

  20. In the ambiguous case, it two triangles are formed with a, b, A, then ...

    Text Solution

    |