Inscribed shapes: find diameter

what I want to do in this video is attempt to find the diameter of this circle right over here I encourage you to pause the video and try this out on your own well let's think about what's going on right over here a B is definitely the diameter of the circle it's a straight line it's going through the center of the circle o is the center of the circle right over here and so what do we know well we could look at this angle right over here angle C and think about it is an inscribed angle and think about the arc that it intercepts it intercepts this arc right over here this arc is exactly half of the circle this arc right over here is exactly half of the circle angle C's inscribed if you take these two sides or the two sides of the angle it intercepts at a and B and so it intercepts an arc this green arc right over here so the central angle right over here is 180 degrees and the inscribed angle is going to be half of that it's going to be 90 degrees or another way of thinking about it it's going to be a right angle and what that does for us is it tells us that triangle ACB triangle a/c B is a right triangle this is a right triangle and the diameter is its hypotenuse so we can just apply the Pythagorean theorem here 15 squared 15 squared plus 8 squared plus 8 squared move to this in magenta plus 8 squared is going to be the length of side a B squared so let me just call this we just called this side right over here let me just call that X that's going to be equal to x squared so 15 squared that's 225 8 squared is 64 plus 64 is equal to x squared I will do that in green is equal to x squared 225 plus 64 is 289 is equal to x squared and then 289 is 17 squared and you could try out a few numbers if you're unsure about that so X is equal to 17 so the diameter or the diameter of the circle right over here is 17