The diameter formsĬase where one edge is sitting on the diameter. Lines as rays, where one of the rays that defines this Is defined, where one on the rays, if you want to view these Out to prove for the special case where our inscribed angle Now we could subtractġ80 from both sides. These three angles mustĪngles of a triangle. That si plus si plus this angle, which is 180 minus Three angles are sitting inside of the same triangle. Together you go 180 degrees around or the kind Supplementary to theta, so it's 180 minus theta. What's this angle going to be? This angle right here. So this is my centralĪngle right there, theta. Si, then you would also know that this angle isĪlso going to be si. See a triangle that looks like this, if I told you this is rĪnd that is r, that these two sides are equal, and if this is Sides being equal, their base angles are also equal. Your circumference is definedīy all of the points that are exactly a radius awayįrom the center. Then this length right here isĪlso going to be the radius of our circle going from theĬenter to the circumference. Here is a radius - that's our radius of our circle. So let me see, this is theĬenter right here of my circle. General case, this is going to be a special case. I'm going to draw an inscribedĪngle, but one of the cords that define it is going to be Or the place I'm going to start, is a special case. Or if I told you that theta wasĨ0 degrees, then you would immediately know that Immediately know that theta must be equal to 50 degrees. Si is equal to, I don't know, 25 degrees, then you would Video is that si is always going to be equal So this angle is si, thisĪngle right here is theta. So that looks like a centralĪngle subtending that same arc. Here - I'll try to eyeball it - that right there is Now, a central angle is anĪngle where the vertex is sitting at the center There, the vertex sitting on the circumference. Subtended by si, where si is that inscribed angle right over It's all very fancy words,īut I think the idea is pretty straightforward. The circumference of the circle that's inside of it, that This angle, it intersects the circle at the other end. That come out from this angle or the two cords that define Words, but I think you'll get what I'm saying. Is going to be exactly 1/2 of the central angle that Use the si for inscribed angle and angles in this video. That's that an inscribed angle is just an angle who's vertex Is to prove one of the more useful results in geometry, and In this case, it means that theta 1 is double than the angle measure of psi one. Follow the same steps as in proof 1, and you recieve 2psi=theta. This then means that the triangle with psi one present means that 2x+(180-theta)=180. And since theta 1 can be used to create one 180 degree line on the diameter in the triangle which has psi one is present, using the angle left of theta 1, it means the angle which is to the left of theta 1, on the diameter is equal to 180-theta. Now, because both sides are to one radius, it means that the triangle is an isosceles triangle, therefore having two equal base angles. Because of this, that side along the ray bordering theta 1 is equal to the radius. For example psi one, has one radius spanning towards the center, and another side which comes from the center of the circle to another point of the circumference of the circle. This means that when we make the diameter across the circle, what it creates is a triangle with two sides equal to the radius. Which means we have to use the first proof to solve the second. 8:04, he says something along the lines of, based on the results I got.
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