# Project 1

### Project 1

AG
##### Ashley Garcia
Ashley's Personal Gallery
##### Transcript
00:00
Let's learn about a very interesting circles theorem!!!!
00:04
The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle’s circumference.
00:20
Consider the following figure, in which an arc (or segment) AB subtends ∠AOB at the center O and ∠ACB at a point C on the circumference.
00:38
We have to prove that ∠AOB = 2 × ∠ACB. Draw the line through O and C, and  let it intersect the circle again at D, as shown.
00:54
There are two triangles formed ΔOAC and ΔOBC. So, we make the following observations. 1. In ΔOAC, ∠OAC = ∠OCA, because OA = OC 2. In ΔOBC, ∠OBC = ∠OCB, because OB = OC. Hence, using the exterior angle theorem, we get, ∠AOD= 2×∠ACO ⋯ (1) ∠DOB= 2×∠OCB ⋯ (2) Add equations (1) and (2): ∠AOD+ ∠DOB= 2× (∠ACO+ ∠OCB) ⇒ ∠AOB= 2× ∠ACB
01:38
I learnt the theorem... That was so easy!!!
01:42
M a t h e m a t i c s A r o u n d U s: PRACTICAL APPLICATION OF THIS THEOREM
01:44
CAMERA: determine the focal length in camera lens VIDEO GAMES :to navigate around objects in video games SCIENCE: The Large Hadron Collider in Europe is a tunnel in the shape of a circle which helps force the particles to move. ARCHITECHTURE: Domes, decorative features in buildings and circular-shaped windows