If `r_(1) +r_(2)+ r = r_(3),` then show that `Delta` is right angled.

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

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

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 r_(1),r_(2) and r_(3) are the position vectors of three collinear points and scalars l and m exists such that r_(3)=lr_(1)+mr_(2) , then show that l+m=1.

Let T be the set of all triangles in a plane with R a relation in T given by R ={(T _(1) , T _(2)): T _(1) is congruent to T _(2) } Show that R is an equivalence relation.

omega is the cube root of 1 and omega ne 1 . Now r_(1), r_(2) and r_(3) are the number obtained while tossing dice thrice. Then ………… is the probability for omega^(r^(1)) +omega^(r^(2))+omega^(r^(3))=0

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

In the circuit shown in figure, epsilon_(1) = 3 V, epsilon_(2) = 2 V , epsilon_(3) = IV and R = r_(1) = r_(2) = r_(3) = 1 Omega . The current through each branch is...... and potential difference between the points A and B 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.

Six resistances each of v ale r= 6Omega are connected between points A,B and C as shown in the figure if R_(1),R_(2) and R_(3) are the net resistances between A and B, between B and C and between A and C respectively, the R_(1):R_(2):R_(3) will be equal to