If `x , ya n dz` are the distances of incenter from the vertices of the triangle `A B C` , respectively, then prove that `(a b c)/(x y z)=cot(A/2)cot(B/2)cot(C/2)`

In a triangle ABc , if r^2cot(A/2) cot(B/2) cot(C/2)=

If in A B C , the distances of the vertices from the orthocentre are x, y, and z, then prove that a/x+b/y+c/z=(a b c)/(x y z)

If A+B+C= pi ,prove that cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2)

Prove that (b + c -a) (cot.(B)/(2) + cot.(C)/(2)) = 2a cot.(A)/(2)

In a Delta ABC, prove that (a + b)/(a - b) = tan ((A + B)/(2)) cot ((A - B)/(2))

If A , B and C are interior angles of a triangle ABC, then show that tan ((A+B) /(2)) =cot ©/(2)

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c)) is -sqrt(3) b. -3sqrt(3) c. sqrt(3) d. 3sqrt(3)

Let z_1, z_2a n dz_3 represent the vertices A ,B ,a n dC of the triangle A B C , respectively, in the Argand plane, such that |z_1|=|z_2|=|z_3|=5. Prove that z_1sin2A+z_2sin2B+z_3sin2C=0.

In a triangle A B C prove that a//(a+c)+b//(c+a)+c//(a+b)<2

For any triangle ABC, prove that (b^2 c^2) cot"A"+"(c^2 a^2)"cot"B""+""(a^2 b^2)" cot"C" "="\ "0