MathDB

Let

S_1, S_2,S_3

be spheres of radii

a, b, c

respectively whose centers lie on a line

l

. Sphere

S_2

is externally tangent to

S_1

and

S_3

, whereas

S_1

and

S_3

have no common points. A straight line t touches each of the spheres, Find the sine of the angle between

l

and

t

Problem Statement