In `A B C ,` right-angled at `C ,` if `tanA=sqrt((sqrt5-1)/2)` , show that the sides `a , ba n dc` are in G.P.

In triangle ABC, right angled at C, (tanA+tanB) equal to

In triangle ABC, if 3(tan'A/2' + tan'C/2') = 2 cot 'B/2 then show that, its sides a,b,c are in A.P.

A tower P Q stands at a point P within the triangular park A B C such that the sides a , ba n dc of the triangle subtend equal angles at P , the foot of the tower. if the tower subtends angles alpha,betaa n dgamma,a tA , Ba n dC respectively, then prove that a^2(cotbeta-cotgamma)+b^2(cotgamma-cotalpha)+a^2(cotalpha-cotbeta)=0

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot

The distance of incentre of the right-angled triangle ABC (right angled at A) from B and C are sqrt10 and sqrt5 , respectively. Then find the perimeter of the triangle.

The angles A, B, C of triangle ABC are in A.P. and b:c = sqrt(3): sqrt(2) . Find A.

If a,b,c are rational numbers and a sqrt(2) +b sqrt(3) + c sqrt(5) = 0 , show that a = b = c = 0

If a, b, c are in G.P. and a^(1//x) = b^(1//y) = c^(1//z) , show that x, y, z are in A.P.

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.

If the three side of a triangle be a, b, c and tan theta=(2 sqrt(ab))/(a-b) "sin"(C)/(2) , then show that "sec" theta =(c)/(a-b) .