Properties and Proportions

Generic Properties

Property 1

In the same circle or in congruent circles, all radii are equal and all diameters are equal

Property 2

If radii are equal, then the circles are congruent

Property 3

If centers of two congruent circles which lie in the same plane are made to coincide, the circles will coincide

Property 4

A point is within, on, or outside of a circle according to its distance from the center is less than, equal to, or greater than, the radius

Property 5

A straight line through any point within a circle cuts the circle at two points

Property 6

Within a given point as center and a given line as radius, one and only one circle can be drawn

Proportion Properties

Proportion 1

In any proportion the product of the means is equal to the product of the extremes

Proportion 2

If the product of two quantities is equal to the product of two other quantities, either pair can be used as means and the other pair extremes

Proportion 3

The mean proportion between two quantities is equal to the square root of their product

Proportion 4

The product of two or more proportions are proportional

Proportion 5

In series of equal ratios, the sum of antecedents, is to the sum of consequents as any antecedent is to its consequent