Geometrii

When I walked by my TV, I noticed this Wii remote wheel. I then wanted to test out the theorem that states that the product of one secant segment and its external segment equals the product of the other secant segment and its external segment. I soon found that the theorem holds true, and the products of the lengths were equal. ~(DM2)

The Truth About Circles

This illustration demonstrates that when you multiply the whole secant by the section outside of the circle, its product is congruent to the other secant multiplied by the other section outside the circle. (~MM2)

Concentric Circles

While going through my bookshelf I noticed that one of my books had an interesting design on it. These circles that are known as Concentric Circles. They all lie in the same plane and have the same center. Also the lines going through the circles are called secants. (~AV5)

Cymbals with Tangents, Chords, & Secants

Over the weekend, I acquired two new cymbals and I thought I'd make use of them, other than for music.  In this first illustration, I proved that the result of multiplying two pieces of individual chords should be equal.  I simply multiplied AE x EC (the labels you can't see very well, sorry,) the first chord, and then BE x ED, the second chord, and they both came out to be 34.36 cm sq.  

In this second picture, I demonstrated that the tangent of a circle multiplied by itself, is equal to the outside piece of a secant multiplied by the entire length of the secant. I squared AB which resulted in 200.77 cm sq, and multiplied AC x AD, which resulted in 200.77 cm sq as well. This proves that the tangent squared does equal the secant length times the outer piece. (~JG2)

GIRL

At my local swimming pool, I found a women's bathroom sign with the shape of a perfect circle and was wondering if I could prove any geometric theorems with it.

On Geometer's Sketchpad, I drew a tangent of the circle and a secant to the circle. I planned to prove theorem 9-10 which states that two secants, two tangents, or a secant and a tangent follow the same equation. The angle that is formed by the intersecting lines would be equivalent to 1/2 the quantity of the major arch created minus the minor arch created.

Through GSP, I have proven that no matter what size or angle, the equation works every time.

(~WM5)