Answer:
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.
A precedent, or an earlier situation or example with similar criteria. stare decisis is Latin for “let the ruling stand” so there for in order to let such ruling stand you must have a precedent to base the situation off. Right now an example would be the Supreme Court being anticipated to overturn the precedent of Roe v. Wade, which has stood for almost 50 years.
Answer to the following question is as follows;
⇒ The Legality of Danny's Proposal;
- In this case, Danny's proposal is regarded an offer until it is approved by Alan in the market. As Danny's promised to sell 100 motorcycles for US$1000 each.
- The proposal from Danny's perspective is an offer since Alan did not acknowledge the agreement in the beginning. Once acknowledged by Allen, this exchanging of bikes becomes an offer.
⇒ Allan's response;
- Allan's response, on the other hand, was interpreted as offer and acceptance because no agreement was reached among them and Allan takes the bike only when it is in good shape.
- If the bikes are not in excellent condition, Allen has the right to decline the seller's contract at any moment.
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Delegates gave the Continental Congress the power to request money from the states and make appropriations, regulating the armed forces, appointing civil servants, and declaring war.
