If p1,\ p2, p3 are the altitudes of a tr...

If `p_1,\ p_2, p_3` are the altitudes of a triangle from the vertices `A , B , C ,\ &\ ` denotes the area of the triangle, prove that `1/(p_1)+1/(p_2)-1/(p_3)=(2a b)/((a+b+c))cos^2C/2`

Topper's Solved these Questions

SOLUTION OF TRIANGLE
MOTION|Exercise EXERCISE - 4( LEVEL I)|4 Videos
SOLUTION OF TRIANGLE
MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos
SOLUTION OF TRIANGLE
MOTION|Exercise EXERCISE - 2 (LEVEL II)|6 Videos
SEQUENCE & SERIES
MOTION|Exercise Exercise -4 Level -II Previous Year /JEE Advanced|22 Videos
STRAIGHT LINE
MOTION|Exercise Exercise 4 Lelvel -II|7 Videos

Similar Questions

Explore conceptually related problems

If p_(1),p_(2),p_(3) are the altitudes 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),p_(3) are altitude of a triangle ABC from the vertices A,B,C and Delta the area of the triangle, then (1)/(p_(1)^(2))+(1)/(p_(2)^(2))+(1)/(p_(3)^(2))=

If p_1,\ p_2,\ p_3 are the altitudes of a triangle from its vertices A ,\ B ,\ C and "Delta" , the area of the triangle A B C , then 1/(p_1)+1/(p_2)-1/(p_3) is equal to s/"Delta" (b) (s-c)/"Delta" (c) (s-b)/"Delta" (d) (s-a)/"Delta"

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 ! the area of the triangle, then p_(1)^(2)+p_(2)^(-2)+p_(3)^(-2) is equal to

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))=

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 p_(1),p_(2),p_(3) are the lengths of the altitudes ofa tringle from the vertices A,B,C,then (1)/(p_(1)^(2))+(1)/(p_(2)^(2))+(1)/(p_(3)^(2))=

If p_(1), p_(2) and p_(3) and are respectively the perpendiculars from the vertices of a triangle to the opposite sides, prove that : (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r ) .

MOTION-SOLUTION OF TRIANGLE-EXERCISE - 3

If in a triangleABC , a = 6, b=3 and cos(A-B)=4/5 then find its area...
Text Solution
|
If in a triangle ABC, /A = 30^@ and the area of triangle (sqrt3a^2)/4 ...
Text Solution
|
If p1,\ p2, p3 are the altitudes of a triangle from the vertices A , B...
Text Solution
|
In a scalene triangle ABC the altitudes AD & CF are dropped from the v...
Text Solution
|
Prove that : (r1-r)/(a) +(r2-r)/(b) = (c )/(r3).
Text Solution
|
Prove that : (r1+r2) tan (C )/(2) = (r3- r) cot ( C)/(2) = c
Text Solution
|
Prove that 2R cos A = 2R + r - r(1)
Text Solution
|
The triangle ABC is a right angled triangle, right angle at A. The rat...
Text Solution
|
The radii r(1), r(2), r(3) of the escribed circles of the triangle ABC...
Text Solution
|
Let a, b and c be the sides of a DeltaABC. If a^2, b^2 and c^2 are t...
Text Solution
|
If D is the mid point of CA in triangle ABC and Delta is the area of t...
Text Solution
|
Show that the radii of the three escribed circles of a triangle are ro...
Text Solution
|
If atanA+btanB=(a+b)tan((A+B)/2) prove that triangle ABC is isosceles.
Text Solution
|
DEF is the triangle formed by joining the points of contact of the inc...
Text Solution
|
DEF is the triangle formed by joining the points of contact of the inc...
Text Solution
|
DEF is the triangle formed by joining the points of contact of the inc...
Text Solution
|
A cyclic quadrilateral A B C D of areal (3sqrt(3))/4 is inscribed in u...
Text Solution
|
If two times the square of the diameter of the circumcircle of a trian...
Text Solution
|
In any triangle ABC, if (cos A + 2 cos C)/(cos A + 2 cos B) = (sin B)/...
Text Solution
|
The triangle ABC (with side lengths a ,b ,c as usual) satisfies loga^2...
Text Solution
|