Rims

Here is something cool I noticed about the rims on this car.

This car's rims form a circle, which also have smaller circles inside of them. 

As you can see, there is one big circle containing five smaller circles. These circles all appear to be similar. I drew radii for all the circles aiming towards the center of the rim, and they appeared to form a pentagon.

I thought it was really cool that this car's rims contained many circles which could form other geometric objects. - (DM5)

Happiest Geometry on Earth

This is an old picture that I took while I was at Disneyland. It is the Mickey Mouse Ferris Wheel. I noticed that it is a perfect example of radii in a circle. Each line goes from the outside to the middle, which is the Mickey Mouse's head. (~CD1)

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)

Angles on a Clock

When I was looking at my clock I noticed that not only could I find the angles made by radii of the triangles but also secants using the theorems in chapter 9. By theorem 9-4 I determined that the measure of angle BCD was equal to the measure of arc BD. From that I was able to use theorem 9-7 to prove the measure of angle BAD is equal to half of arc BD. Therefore the measure of angle BAD is equal to half of the measure of  angle BCD. (~AL1)

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)

Books

This is a picture of a bunch of different symbols from books put together (Percy Jackson, Harry Potter, The Mortal Instruments, The Hunger Games, Divergent).

In this picture, there are three circles. The center one is externally tangent to both of the circles on either side of it. The vertical line in the middle of the picture is also the diameter of the center circle.

This image also has two lines that are externally tangent to the center circle (lines j and k). The right angles formed by the radii to the tangency point prove that the lines are tangent.

~CS1

Congruent Tangents

GC2

Tangents to a circle from a point are congruent. (Corollary)

I brought my camera to an ice cream parlor last week in hopes of finding an example of the corollary stated above. According to this corollary, tangents to a circle from a point are congruent. I found my ice cream cone to be a great example of this. In the picture, segments AB and AC are both tangent to the circle (scoop) at points B and C. This should assure that tangent AB is congruent to tangent AC, which was further proven when I measured the segments using GSP.