If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are `alpha,betaa n dgamma` then prove that `r^2=(alphabetagamma)/(alpha=beta+gamma)`

If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are alpha,beta and gamma then prove that r^(2)=(alpha beta gamma)/(alpha=beta+gamma)

If the distances of the vertices of a triangle from the point of contact of the incricle with the sides be alpha,beta,gamma then r is equal to (where r=inradius)

If alpha,beta,gamma,in(0,(pi)/(2)), then prove that (si(alpha+beta+gamma))/(sin alpha+sin beta+sin gamma)<1

Let A(3,4) B(5,0), C(0,5) be the vertices of a triangle ABC then orthocentre of Delta ABC is (alpha, beta) Find alpha + beta

If origin is the orthocenter of a triangle formed by the points (cos alpha*sin alpha,0)*(cos beta,sin beta.0),(cos gamma,sin gamma,0) then sum cos(2 alpha-beta-gamma)=

Distance of the point (alpha, beta, gamma) , from z-axis is

A variable plane is at a constant distance 3p from the origin and meets the coordinates axes in A,B and C if the centroid of triangle ABC is (alpha,beta,gamma ) then show that alpha^(-2)+beta^(-2)+gamma^(-2)=p^(-2)

The ratios of the length of the sides BC and AC of Delta ABC to the radius of circumscribea cirere are equal to 2 and respectively.If the ratio of the lengths of the bisectors of the interior angles B and C is (alpha(sqrt(alpha)-1))/(beta sqrt(gamma)) where alpha,beta,gamma in N, then find the value of (alpha+beta+gamma).