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 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).

The lengths of the tangents drawn from the vertices A,B,C to the incircle of Delta ABC are 5,3,2 respectively.If the lengths of the parts of tangents within the triangle which are drawn parallel tothe sides BC,CA,AB of the triangle to the incirclebe alpha,beta,gamma respectively then (10)/(31)(alpha+beta+gamma) equals