If the sides of a triangle are in A.P., ...

If the sides of a triangle are in A.P., and its greatest angle exceeds the least angle by `alpha`, show that the sides are in the ratio `1+x :1:1-x`, , where `x = sqrt((1- cos alpha)/(7 - cos alpha))`

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 the sides of a triangle are in A.P. and the greatest angle of the triangle exceeds the least by 90^(@) , then sine of the third angle is

The sides of a right angled triangle arein A.P. , then they are in the ratio

If the angles of a triangle are in A.P.with common difference equal 1//3 of the least angle ,the sides are in the ratio

The sides of a triangle are in the ratio 1: sqrt3:2. Then the angles are in the ratio

The sides of a triangle are in A.P. and its area is 3/5t h of the an equilateral triangle of the same perimeter, prove that its sides are in the ratio 3:5:7, and find the greatest angle of the triangle.

The sides of a triangle are x^2+x+1, 2x+1 and x^2-1. Prove that the greatest angle is 120^0

The sides of a triangle ABC are (x^(2) + x +1),(2x+1) and (x^(2)-1) . Find the greatest angle of the triangle.

If the sides of a triangle are in the ratio 1 : sqrt(2) : 1 , show that it is a right-angled triangle.

The sides of a triangle are x^2+x+1,2x+1,a n dx^2-1 . Prove that the greatest angle is 120^0dot

If the angle opf a triangle are in the ratio 1:2:3, then show that the sides opposite to the respective angle are in the ratio 1: sqrt3:2.

VMC MODULES ENGLISH-PROPERTIES OF TRIANGLE-Level - 2

Statement I If the sides of a triangle are 13, 14 15 then the radius o...
Text Solution
|
Statement I In a DeltaABC, sum (cos ^(2)""(A)/(2))/(a ) has the value...
Text Solution
|
If the sides of a triangle are in A.P., and its greatest angle exceeds...
Text Solution
|
If r(1), r(2) ,r(3) are the ex-radii of DeltaABC, then prove that (b...
Text Solution
|
If r and R are radii of the incircle and circum-circle of DeltaABC, t...
Text Solution
|
If A is the area and 2s is the sum of the sides of a triangle, then Al...
Text Solution
|
In DeltaABC, (a^(2)+b^(2))/(a^(2)-b^(2))=(sin(A+B))/(sin(A-B)), prove ...
Text Solution
|
The sides of a triangle are in AP. If the angles A and C are the great...
Text Solution
|
perpendiculars are drawn from the angles A , Ba n dC of an acute-angle...
Text Solution
|
If cos theta=(a)/(b+c),cos phi=(b)/(a+c),cospsi=(c)/(a+b), where theat...
Text Solution
|
Given the base of a triangle, the opposite angle A, and the product k^...
Text Solution
|
If a,b,c are in HP, then prove that sin ^(2) ""(A)/(2), sin ^(2) ""(B)...
Text Solution
|
If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the ...
Text Solution
|
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
|