Three circles with centres `C_1, C_2 and C_3` and radii `r_1, r_2 and r_3` where `r_1

There circle C_1,C_2 and C_3 with radii r_1 , r_2 and r_3 (where r_1 तीन वृत्त C_1,C_2 तथा C_3 जिनको त्रिज्याएँ r_1 , r_2 तथा r_3 है, (जहाँ r_1

Three circle C_(1),C_(2)andC_(3) with radii r_(1),r_(2) and r_(3) (where r_(1)ltr_(2)ltr_(3) ) are placed as shown in the given figure. What is the value of r_(2) ?

Two circles with centres at C_(1) , C_(2) and having radii r_(1) , r_(2) will intersect each in two real distinct points if , and only if :

Consider a series of 'n' concentric circles C_1, C_2, C_3, ....., C_n with radii r_1, r_2, r_3, ......,r_n respectively, satisfying r_1 > r_2 > r_3.... > r_n and r_1= 10. The circles are such that the chord of contact of tangents from any point on C_1 to C_(i+1) is a tangent to C_(i+2) (i = 1, 2, 3,...). Find the value of lim_(n->oo) sum_(i=1)^n r_1, if the angle between the tangents from any point of C_1 to C_2 is pi/3.

Three circles C_(1),C_(2),C_(3) with radii r_(1),r_(2),r_(3)(r_(1)ltr_(2)ltr_(3)) respectively are given as r_(1)=2 , and r_(3)=8 they are placed such that C_(2) lines to the right of C_(1) and touches it externally C_(3) lies ot the right of C_(2) and touches it externally. There exist two stratight lines each of whic is a direct common tangent simultaneously to all the three circles then r_(2) is equal to

Three circles C_(1),C_(2),C_(3) with radii r_(1),r_(2),r_(3)(r_(1)ltr_(2)ltr_(3)) respectively are given as r_(1)=2 , and r_(3)=8 they are placed such that C_(2) lines to the right of C_(1) and touches it externally C_(3) lies ot the right of C_(2) and touches it externally. There exist two stratight lines each of whic is a direct common tangent simultaneously to all the three circles then r_(2) is equal to