If in a triangle `(1-(r_1)/(r_2))(1-(r_1)/(r_3))=2` then the triangle is right angled (b) isosceles equilateral (d) none of these

If in a triangle r_1=r_2+r_3+r , prove that the triangle is right angled.

In a triangle, if r_(1) gt r_(2) gt r_(3), then show a gtb gt c.

In any triangle. if(a^2-b^2)/(a^2+b^2)=("sin"(A-B))/("sin"(A+B)) , then prove that the triangle is either right angled or isosceles.

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

In a right angles triangle, prove that r+2R=s.

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((z y)/(x r))+tan^(-1)((x z)/(y r))+tan^(-1)((x y)/(z r)) is equal to pi (b) pi/2 (c) 0 (d) none of these

Write ‘True’ or ‘False’ and justify your answer: The volume of the frustum of a cone (1)/(3)pi h(r_(1)^(2)+r_(2)^(2)-r_(1)r_(2)) where h is the vertical height of the frustum and r_(1),r_(2) are the radii of the ends.

((n),(r))+((n),(r-1))=((n+1),(r-1))

Statement I In a Delta ABC, if a lt b lt c and ri si inradius and r_(1), r_(2) ,r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

Supposing Newton's Law of gravitation for gravitation forces F_1 and F_2 between two masses my and m, at positions r_1 and r_2 read F_1=-F_2=-(r_(12))/(r_(12^3))GM_0^2((m_1m_2)/(M_0^2))^(2) where M_0 is a constant of dimension of mass, r_(12) =r_1 -r_2 and n is a number. In such a case,