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 a right angle triangle ABC, right angle is at B ,If tan A=sqrt(3) , then find the value of (i) sin A cos C+ cos A sin C " "(ii) cos A cos C -sin A sin C

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

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

In a triangle A B C , right angled at A , on the leg A C as diameter, a semicircle is described. If a chord joins A with the point of intersection D of the hypotenuse and the semicircle, then the length of A C is equal to (a) (A B.A D)/(sqrt(A B^2+A D^2)) (b) (A B.A D)/(A B+A D) (c) sqrt(A B.A D) (d) (A B.A D)/(sqrt(A B^2-A D^2))

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 angle A ,Ba n dC of a triangle are in an arithmetic propression and if a , ba n dc denote the lengths of the sides opposite to A ,Ba n dC respectively, then the value of the expression a/csin2C+c/asin2A is 1/2 (b) (sqrt(3))/2 (c) 1 (d) sqrt(3)