In a scalene triangle `A B C ,D` is a point on the side `A B` such that `C D^2=A D D B ,` sin `s in A S in B=sin^2C/2` then prove that CD is internal bisector of `/_Cdot`

In a triangle ABC, D is a point on BC such that AD is the internal bisector of angle A . Let angle B = 2 angle C and CD = AB. Then angle A is

In triangle A B C ,D is on A C such that A D=B C=D C ,/_D B C=2x ,a n d/_B A D=3x , all angles are in degrees, then find the value of xdot

In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B) , then prove that cos 2A,cos2B and cos 2C are in AP.

Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E is the foot of the perpendicular drawn from D to A C ,a n dF is the midpoint of D E , then prove that A F is perpendicular to B Edot

If A + B + C = 2s, then prove that sin (s - A) sin (s - B) + sin s. sin (s - C) = sin A sin B .

In a triangle ABC, prove that b^(2) sin 2C+c^(2) sin 2B=2bc sin A .

In A B C , on the side B C ,Da n dE are two points such that B D=D E=E Cdot Also /_A D E=/_A E D=alpha, then

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))

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

If sides of triangle A B C are a , ba n dc such that 2b=a+c then b/c >2/3 (b) b/c >1/3 b/c<2 (d) b/c<3/2