In a triangle ABC,if `1/r_1^2+1/r_2^2+1/r_3^2+1/r^2=`

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

In a triangle ABC I_1, I_2,I_3 are excentre of triangle then show that II_(1). II_(2). II_(3)=16R^(2)r.

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

In DeltaABC, let b=6, c=10and r_(1) =r_(2)+r_(3)+r then find area of Delta ABC.

Centroid of the triangle with verticies P(1, -2, 1), Q(2, 3, -1) and R(1, -1, -1) is _____ .

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.

The equivalent resistance (R_s) of a series combination of resistors is given by 1/R_s = 1/R_1 + 1/R_2 + …………. .

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,

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)

If in a triangle of base 'a', the ratio of the other two sides is r ( <1).Show that the altitude of the triangle is less than or equal to (ar)/(1-r^2)