Let f, g and h be the lengths of the per...

Let `f, g and h` be the lengths of the perpendiculars from the circumcenter of `Delta ABC` on the sides a, b, and c, respectively. Prove that `(a)/(f) + (b)/(g) + (c)/(h) = (1)/(4) (abc)/(fgh)`

`(1)/(4)`

`(1)/(2)`

`1`

`2`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

SOLUTION OF TRIANGLE
MOTION|Exercise EXERCISE - 2 (LEVEL I)|25 Videos
SOLUTION OF TRIANGLE
MOTION|Exercise EXERCISE - 2 (LEVEL II)|6 Videos
SOLUTION OF TRIANGLE
MOTION|Exercise EXERCISE - 4( LEVEL II)|10 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

Let f,g,h be the lengths of the perpendiculars from the circumcenter of the Delta ABC on the sides BC,CA and AB respectively.If (a)/(f)+(b)/(g)+(c)/(h)=lambda(abc)/(fgh), then the value of 'lambda' is (B) (1)/(2) (B) (1)/(2) (D) (1)/(2) (D) 2

If x,y,z are respectively perpendiculars from the circumcentre on the sides of the Delta ABC, the value of (a)/(x)+(b)/(y)+(c)/(z)-(abc)/(4xyz)=

If BM and CN are the perpendiculars drawn on the sides AC and BC of the Delta ABC , prove that the points B, C, M and N are concyclic.

In Delta ABC,a,b,c are the opposite sides of the angles A,B and C respectively,then prove (sin B)/(sin(B+C))=(b)/(a)

AD, BE and CF are the medians of triangle ABC whose centroid is G. If the points A, F, G and E are concyclic, then prove that 2a^(2) = b^(2) + c^(2)

If ABC is an isosceles triangle with AB=AC .Prove that the perpendiculars from the vertices B and C to their opposite sides are equal.

If in Delta ABC, b = 3 cm, c = 4 cm and the length of the perpendicular from A to the side BC is 2 cm, then how many such triangle are possible ?

In a acute angled triangle ABC, proint D, E and F are the feet of the perpendiculars from A,B and C onto BC, AC and AB, respectively. H is orthocentre. If sinA=3/5a n dB C=39 , then find the length of A H

If g, h, k denotes the side of a pedal triangle, then prove that (g)/(a^(2))+ (h)/(b^(2))+ (k)/(c^(2))=(a^(2)+b^(2) +c^(2))/(2 abc)

MOTION-SOLUTION OF TRIANGLE-EXERCISE -1

In A B C , the median A D divides /B A C such that /B A D :/C A D=2:1...
Text Solution
|
If the median AD of triangle ABC makes an angle pi/4 with the side BC,...
Text Solution
|
In a DeltaABC, A=(2pi)/3, b-c=3sqrt3 cm and area(DeltaABC)=(9sqrt3)/2 ...
Text Solution
|
If the area of triangleABC is triangle =a^(2) -(b-c)^(2), then: tanA =
Text Solution
|
If the sides of a triangles are 3:7:8, then ratio R:r
Text Solution
|
In a right angled triangle R is equal to
Text Solution
|
In a triangle a = 13 , b = 14, c = 15, r =
Text Solution
|
In an equilateral triangle, the inradius and the circumradius are conn...
Text Solution
|
In a triangle ABC, right angled at B, then
Text Solution
|
If the area of triangles is 100 sq. cm, r1= 10 cm and r2= 50 cm, then...
Text Solution
|
In a triangleABC, the inradius and three exradii are r,r1,r2" and "r3 ...
Text Solution
|
In a triangleABC if r1 lt r2 lt r3, then
Text Solution
|
In a triangle ABC, if (a-b)/(b-c)= (s-a)/(s-c), then r1,r2,r3 are in
Text Solution
|
If AD, BE and CF are the medians of a ABC ,then (AD^(2)+BE^(2)+CF^(2))...
Text Solution
|
In triangle ABC, line joining the circumcenter and orthocenter is para...
Text Solution
|
In a triangle ABC, angle A = 30^(2), BC = 2 + sqrt5, then find the dis...
Text Solution
|
If in triangle A B C ,sumsinA/2=6/5a n dsumI I1=9 (where I1,I2a n dI3 ...
Text Solution
|
If in a triangle A B C , right angle at B ,s-a=3a n ds-c=2, then a=2,c...
Text Solution
|
If H is the orthocentre of a triangle ABC, then the radii of the circl...
Text Solution
|
Let f, g and h be the lengths of the perpendiculars from the circumcen...
Text Solution
|