Why is ratio of |AB|/|BC| always the same?

How many comon points have these three cir c les?

>>7644493
2

>>7644493
Infinity pointa in comum

because it is defined that way stupid fuck, there is no "why" in math, it is all a consequence of our axioms. Anyone that looks for a "why" is just a scrub that believes intuition is anything more than a posteriori projection.

>>7645024
it should have been clear to you what he means if you didn't have autism. he was just looking for further explanation of the result so he could understand it more comprehensively.
also was it necessary to be rude?

File: Sodium Polyacrylate.gif (983KB, 290x211px) Image search: [Google]

983KB, 290x211px

>>7645050
kek. Nice one, man. I'm glad there are a few people like you on this board.

>>7645024
>because it is defined that way
you are retarded

>>7645274
How much heat does that release?

>>7645274
Mother fucking easy snow!

File: Pencil of circles-01.png (59KB, 1700x864px) Image search: [Google]

59KB, 1700x864px

>>7644454
Let OAaP, OBbP, and OCcP be distinct circles sharing the two points O and P.

As a consequence of the the inscribed angle theorem, we have ∠OAP = ∠OaP, ∠OBP = ∠ObP, and ∠OCP = ∠OcP. Furthermore, because ∠ABO = ∠abO and ∠BCO = ∠bcO, we also see that ∠AOB = ∠aOb and ∠BOC = ∠bOc.

Hence, triangles AOB and aOb are similar. Likewise the same can be said of triangles BOC and bOc.

By the similarity of triangles AOB and aOb, we infer that |AB|/|ab| = |OB/|ob|. Similarly, the similarity of triangles BOC and bOc implies |BC|/|bc| = |OB|/|ob|.

Therefore |AB|/|ab| = |BC|/|bc| or |AB|/|BC| = |ab|/|bc|.

>>7645335
Hardly any

>>7645465
Thank you very much