Home
Class 12
MATHS
If the lengths of the perpendiculars fro...

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))`.

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Sesssion 5|7 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Sesssion 6|4 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Sesssion 3|34 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 p_(1),p_(2),p_(3) are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that p_(1)p_(2)p_(3)=(a^(2)b^(2)c^(2))/(8R^(3))

If p_(1), p_(2),p_(3) are respectively the perpendiculars from the vertices of a triangle to the opposite sides , then (cosA)/(p_(1))+(cosB)/(p_(2))+(cosC)/(p_(3)) is equal to

If p_(1), p _(2), p_(3) are respectively the perpendicular from the vertices of a triangle to the opposite sides, then find the value of p_(1) p_(2)p _(3).

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)

Let the lengths of the altitudes from the vertices A(-1, 1), B(5, 2), C(3, -1) of DeltaABC are p_(1), p_(2), p_(3) units respectively then the value of (((1)/(p_(1)))^(2)+((1)/(p_(3)))^(2))/(((1)/(p_(2)))^(2)) is equal to

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 : q = 1(1)/(3) : 1(1)/(2) and q : r = (1)/(2) : (1)/(3) , find p : r

Prove that: (i) (.^(n)P_(r))/(.^(n)P_(r-2)) = (n-r+1) (n-r+2)

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 r_(1), r_(2), r_(3) in triangle be in H.P., then the sides are :