on the blank spaces, analyze the concentric circles and write a short interpretation based on your understanding

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric by inversion by picking the inversion center as one of the limiting points.

1. Picking any two points on the outer circle and connecting them gives 1/3.

2. Picking any random point on a diagonal and then picking the chord that perpendicularly bisects it gives 1/2.

3. Picking any point on the large circle, drawing a line to the center, and then drawing the perpendicularly bisected chord gives 1/4.

So some care is obviously needed in specifying what is meant by "random" in this problem.

Given an arbitrary chord BB^' to the larger of two concentric circles centered on O, the distance between inner and outer intersections is equal on both sides (AB=A^'B^'). To prove this, take the perpendicular to BB^' passing through O and crossing at P. By symmetry, it must be true that PA and PA^' are equal. Similarly, PB and PB^' must be equal. Therefore, PB-PA=AB equals PB^'-PA^'=A^'B^'. Incidentally, this is also true for homeoids, but the proof is nontrivial.

answer:

the colonists had their reasons for creating a weak central (federal) government under the articles of confederation. not only did they create a weak federal government, they restricted the powers of the state governors because they were so concerned about the leaders abusing their power.

answer:

hi i'm turkish!  

baklava  

kuru pilav

şöbiyet

hi i'm turkish!

hi i'm turkish!  

baklava  

kuru pilav

şöbiyet

hi i'm turkish!

baklava

çi̇ki̇ çi̇ki̇ta adarrr** ajdar***

explanation: