Circle geometry12/19/2023 ![]() SemicircleĪnd of course, an arc with a measure of 180 degrees we call a semicircle. So that’s 180 degrees on each side and so that divides the circle into two 180 degree arcs. As we go from A, to O, to B, it’s a straight line, we don’t bend at all. Now a diameter is essentially a 180 degree angle. Diameterīecause the angle equals 135 degrees, that automatically means that the arc from J to K to L is also a 135 degree arc. So for example here, we have this arc that goes from J to K to L, and we have the angle. The measure of a central angle equals the measure of the arc. One way to talk about the size of an arc is to talk about it’s arc measure, that is how many degrees it has. A central angle has a unique relationship with the arc it intersections. Central AngleĪn angle with its vertex at the center of the circle is called a central angle. Now notice that that angle at the middle, angle EOF, has its vertex at the center of the circle. So that necessarily means that that third chord would have to have a length equal to the length of the radius. We know if we draw the third cord we will have an isosceles triangle. Alternately, if we are given two radii and a 60 degree angle between them. So if we are told that that cord EF, also has a length of R in addition to a few radii, well then immediately we know we have a equilateral triangle and we have 360 degrees angles. If the chord side of such a triangle is also equal to the radius, then the triangle would be equilateral, which of course is a special case of isosceles. ![]() So that means we have to have an angle of 70 degrees at B, which leaves 40 degrees for the angle at O. And so that we have an angle of 70 degrees at A. And because the sides are equal the angles have to be equal. Well, right away that means we have a triangle with two equal sides, in other words an isosceles triangle. ![]() Of course, if we look at this triangle here OB and OA are radii–so of course they’re equal because all radii of the same circle are equal. Now that is pretty obvious when you think about it. Any triangle with two sides that are radii have to be isosceles. The first one that we are gonna talk about is lengths and this is relatively easy. Many of the properties that we will talk about in this video will involve angles in circles. Now we can talk about some circle properties. Transcript: Circle Properties Angles in Circles
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