If the sides of triangle in A.P. and `/_C=90+/_A` then prove that sides will be in ratio `sqrt7+1:sqrt7:sqrt7-1`

If the angles of a triangle are in the ratio 2 : 3 : 7 ,then the sides are in the ratio

Prove that 5sqrt(7) is irrational.

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

If the cotangents of half the angles of a triangle are in A.P., then prove that the sides are in A.P.

If the sides of triangle are in the ratio 3 : 5 : 7 , then prove that the minimum distance of the circumcentre from the side of triangle is half the circmradius

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))

If the sides of a right-angled triangle are in A.P., then the sines of the acute angles are 3/5,4/5 b. 1/(sqrt(3)),sqrt(2/3) c. 1/2,(sqrt(3))/2 d. none of these

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.

If a ,b ,c are in A.P., then prove that the following are also in A.P. 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.