[" 3.If "r<1" and positive and "m" is a positive integer,shew that "],[qquad (2m+1)r^(m)(1-r)<1-r^(2m+1)]

Let ABC be a triangle with incentre I and inradius r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB, respectively, If r_(2)" and "r_(3) are the radii of circles inscribed in the quadrilaterls AFIE, BDIF and CEID respectively, then prove that r_(1)/(r-r_(1))+r_(2)/(r-r_(2))+r_(3)/(r-r_(3))=(r_(1)r_(2)r_(3))/((r-r_(1))(r-r_(2))(r-r_(3)))

Let ABC be a triangle with incentre I and inradius r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB, respectively, If r_(2)" and "r_(3) are the radii of circles inscribed in the quadrilaterls AFIE, BDIF and CEID respectively, then prove that r_(1)/(r-r_(1))+r_(2)/(r-r_(2))+r_(3)/(r-r_(3))=(r_(1)r_(2)r_(3))/((r-r_(1))(r-r_(2))(r-r_(3)))

The combined resistance R of two resistors R_1 and R_2(R_1,R_2>0) is given by 1/R=1/R_1+1/R_2 . If R_1+R_2=C (a constant), show that the maximum resistance R is obtained by choosing R_1=R_2 .

Show that +" ":" "R" "xx" "R ->R and xx" ":" "R" "xx" "R ->R are commutative binary operations, but " ":" "RxxR ->R and -:" ":" "R_* xxR_* ->R_* are not commutative.

If r_(1)^(2)=r_1r_(2)+r_(2)r_(3)+r_(3)r_(1) then the triangle is

If Delta(r)=|{:(r,r+1),(r+3,r+4):}| then expand it

If Delta(r)=|{:(r,r+1),(r+3,r+4):}| then expand it

If Delta(r)=|{:(r,r+1),(r+3,r+4):}| then expand it

If (r)/(r_(2))=(r_(1))/(r_(3)) then