`R=(r^(2)s^(2))/(4)((1)/(r)-(1)/(r_(1)))((1)/(r)-(1)/(r_(2)))((1)/(r)-(1)/(r_(3)))`

Show that ((1)/(r _(1))+ (1)/(r_(2)))((1)/(r_(2))+(1)/(r _(3)))((1)/(r _(3))+(1)/(r_(1)))=(64 R^(3))/(a ^(2)b^(2) c^(2))

(r_(2)+r_(3))sqrt((r r_(1))/(r_(2)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)))

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: S_1+S_2+S_3+..+S_n= (A) (na)/(1-r)-(ar(1-r^n))/((1-r)^2 (B) (na)/(1-r)-(ar(1+r^n))/((1+r)^2 (C) (na)/(1-r)-(a(1-r^n))/((1-r)^2 (D) none of these

The value of 1/(r_(1)^(2))+1/(r_(2)^(2))+1/(r_(2)^(3))+1/(r^(2)) , is

Prove that : 1/(r_1)+1/(r_2)+1/(r_3)=1/r

Value of 1/(r_(1)^2)'+ 1/(r_(2)^2)+ 1/(r_(3)^2)+ 1/(r_()^2) is :

The circles having radii r_1a n dr_2 intersect orthogonally. The length of their common chord is (2r_1r_2)/(sqrt(r1^2+r2^2)) (b) (sqrt(r1^2+r2^2))/(2r_1r_2) (r_1r_2)/(sqrt(r1^2+r1^2)) (d) (sqrt(r1^2+r1^2))/(r_1r_2)

If r_(1), r_(2), r_(3) are radii of the escribed circles of a triangle ABC and r it the radius of its incircle, then the root(s) of the equation x^(2)-r(r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1))x+(r_(1)r_(2)r_(3)-1)=0 is/are :

The conbined resistance R of two resistors R,& R_(2)(R_(1),R_(2) gt 0) is given by . (1)/(R)=(1)/(R_(1)) +(1)/(R_(2)). If R_(1)+R_(2)= constant Prove that the maximum resistance R is obtained by choosing R_(1)=R_(2)