Question

Geometry question

Answer 1

Find \(AB\) in terms of \(r_1,r_2\quad and\quad OO'\)

segment \(AB\) is common transverse tangent

Answer 2

In right triangle OO'C :
\[OC^2 = d^2-(r_1+r_2)^2\]

Answer 3

therefore\[AB=OC=\sqrt{d^2-(r_1+r_2)^2}\]

Answer 4

that construction makes it look very easy

Answer 5

thnks

Answer 6

same thing

Answer 7

Yeah, the circles are totally just red herrings trying to fool you, it's basically a conspiracy that every geometry problem ends up really just being about the pythagorean theorem or triangles haha.