In a `DeltaABC,` show that `r_(1)* r_(2)* r_(3)*r=Delta^(2).`

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.

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

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)

The distance between two particles of masses m_(1)andm_(2) is r. If the distance of these particles from the centre of mass of the system are r_(1)andr_(2) respectively, then show that r_(1)=r((m_(2))/(m_(1)+m_(2)))andr_(2)=r((m_(1))/(m_(1)+m_(2)))

Prove that if two bubbles of radii r_(1) and r_(2)(r_(1)ltr_(2)) come in contact with each other then the radius of curvature of the common surface r=(r_(1)r_(2))/(r_(2)-r_(1))

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

If R_1 and R_2 are equivalence relations in a set A, show that R_(1) cap R_2 is also an equivalence relation.

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