A triangle A B C is inscribed in a circl...

A triangle `A B C` is inscribed in a circle with centre at `O ,` The lines `A O ,B Oa n dC O` meet the opposite sides at `D , E ,a n dF ,` respectively. Prove that `1/(A D)+1/(B E)+1/(C F)=(acosA+bcosB+ccosC)/triangle`

Text Solution

Verified by Experts

The correct Answer is:

2

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

In quadrilateral A B C D ,\ A O\ a n d\ B O are the bisectors of /_A\ a n d\ /_B respectively. Prove that /_A O B=1/2(/_C+/_D)dot

O is any point inside a triangle A B C . The bisector of /_A O B ,/_B O C and /_C O A meet the sides A B ,B C and C A in point D ,E and F respectively. Show that A D * B E * C F=D B * E C * F A

In an isosceles triangle A B C with A B=A C , a circle passing through B\ a n d\ C intersects the sides A B\ a n d\ A C at D\ a n d\ E respectively. Prove that D E || B C .

In a quadrilateral A B C D ,\ C O\ a n d\ D O are the bisectors of /_C\ a n d\ /_D respectively. Prove that /_C O D=1/2(/_A+/_B)dot

A B C D is a tetrahedron and O is any point. If the lines joining O to the vertices meet the opposite faces at P ,Q ,Ra n dS , prove that (O P)/(A P)+(O Q)/(B Q)+(O R)/(C R)+(O S)/(D S)=1.

The bisectors of the angles B and C of a triangle A B C , meet the opposite sides in D and E respectively. If DE||BC , prove that the triangle is isosceles.

In a circle with centre O , chords A B\ a n d\ C D intersect inside the circumference at E . Prove that /_A O C+\ /_B O D=2\ /_A E C

In a circle with centre O , chords A Ba n dC D intersect inside the circumference at Edot Prove that /_A O C+/_B O D=2/_A E Cdot

If D ,E and F are three points on the sides B C ,CA and A B , respectively, of a triangle A B C show that the (B D)/(C D)=(C E)/(A E)=(A F)/(B F)=-1

VMC MODULES ENGLISH-PROPERTIES OF TRIANGLE-Level - 2

Consider the following statements concerning a DeltaABC (i) The sid...
Text Solution
|
Prove that a triangle A B C is equilateral if and only if tanA+tanB+ta...
Text Solution
|
Let ABC be a triangle having O and I as its circumcentre and incentre,...
Text Solution
|
Let ABC be a triangle with incenter I and inradius r. Let D, E, and F ...
Text Solution
|
If In is the area of n-s i d e d regular polygon inscribed in a cir...
Text Solution
|
In a DeltaABC, if r(1) +r=r(2), then find the vlaue of (sec ^(2) A + c...
Text Solution
|
In DeltaABC, let b=6, c=10and r(1) =r(2)+r(3)+r then find area of Delt...
Text Solution
|
Consider on obtuse angle triangles with side 8 cm, 15 cm and xx cm (la...
Text Solution
|
letABC be a right angled triangle at C. If the inscribed circle touche...
Text Solution
|
Consider a Delta ABC and let a,b, and c denote the leghts of the sides...
Text Solution
|
In a DeltaABC, the internal bisector of angle ABC meets AC at k. if BC...
Text Solution
|
In DeltaABC has AC=13, AB=15 and BC=14. Let O be the circumcenter of t...
Text Solution
|
With usual notation in Delta ABC, the numerical value of ((a+b+c)/(r...
Text Solution
|
In a Delta ABC, cos A. cos C = (lambda(c^(2) - a^(2)))/(3 ca), if is t...
Text Solution
|
In a triangle ABC, medians AD and CE are drawn. If AD=5, angle DAC=pi/...
Text Solution
|
In a DeltaABC, the maximum value of 120((sum a cos ^(2)((A)/(2)))/(a+...
Text Solution
|
In DeltaABC, angle C = 2 angle A, and AC = 2BC, then the value of (a^(...
Text Solution
|
If a, b and A are given in a triangle and c(1), c(2) are possible valu...
Text Solution
|
A triangle A B C is inscribed in a circle with centre at O , The lines...
Text Solution
|
In a triangle ABC, a ge b ge c. If (a^(3)+b^(3)+c^(3))/(sin ^(3)A +s...
Text Solution
|