ABC is a fixed right angled isosceles triangle right angled at B. Pis a variable point inside the triangle whose distances from the sides `AB,BC and CA` are `alpha,beta-gamma` respectively. If `alpha^2 + beta^2+alpha beta=gamma^2`, then the locus of P=

In a Delta ABC, D,E and F respectively are the points of contact of the incircle with the sides AB, BC and CA such that AD =alpha, BE= beta and CF =gamma," then "(alpha beta gamma)/(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 alpha,beta, gamma are the lengths of altitudes of Delta ABC , then alpha^-2+ beta^-2+ gamma^-2 =

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

If the sides of a right angled triangle are {cos 2 alpha + cos 2 beta + 2 cos (alpha+beta)} and {sin 2 alpha+sin 2 beta + 2 sin (alpha+beta)} then the length of the hypotneuse is

If the sides of a right angled triangle are {cos 2 alpha + cos 2 beta + 2 cos (alpha+beta)} and {sin 2 alpha+sin 2 beta + 2 sin (alpha+beta)} then the length of the hypotneuse 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)

In a right angle triangle ABC, alpha and beta are the two angles other than right angle, if beta = 30^(@) , then what is tan alpha equal to?