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## High school geometry

### Course: High school geometry>Unit 8

Lesson 1: Circle basics

# Circles glossary

Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs. Created by Sal Khan.

## Want to join the conversation?

• Do you always need 3 letters for a major arc? •   Yes. if you only had 2 points, it would be a minor arc. If you had 3 or more points, you could have a major arc and some minor arcs!
• Is there a way that you can measure the 'degree' of an arc? Like how 'narrow' or 'stretched out' it is? •   The corresponding central angle is the angle formed by any two radii of a circle. For example, at , consider the arc JK. Imagine you're cutting out a pie piece with the radii JB and KB. The central angle that corresponds to the arc JK would be JBK. If we know that central angle, we know that the arc's degree measurement is the same. So if the angle JBK is 56º, the arc JK is also 56º.
• This question does not necessarily pertain to this video, but I don't know where else to put this. I understand that it takes 2 points to define a line, and three to define the circumference of a circle, but how many define a parabola? It can't be two, and three doesn't make sense either. •   The rules for quadratic functions are the same as the rules for circles. Given any three points that aren't on the same line and with no two points on the same vertical line, there is exactly one quadratic function whose graph passes though those three points.

I don't want to get too weird, but parabolas are a little more complicated. We talk about a parabola as being the locus of points that are the same distance from a given point and a given line, but nearly all the time we only consider the case when that line is horizontal. If you're okay with the line not being horizontal, then you're going to get shapes that aren't the graph of a function, but a circle isn't the graph of a function either because lots of vertical lines cross it in more than one point. With this more flexible notion of what a parabola is, now it would generally take FOUR points to define the parabola, and there are a couple of extra exceptions beyond the fact that no three of them can be on a straight line. (For instance, the four corners of a square cannot lie on any legitimate parabola no matter which way the directrix is facing.) Hope that wasn't too far afield for you!
• Does a circle have any sides? • so is the circumference only used for circles? and why? •  It's the measure of the outline of the shape. This concept is used in other shapes, but called perimeter. Circumference is special to a circle (the "circ" at the beginning is a clue), (though the phrase can be used for ellipses too). One reason circumference is special it that it involves π, being the ratio of the diameter to the circumference. This special relationship isn't found for squares, rectangles, etc.
• at , he says that the shortest distance was called a minor arc and the longest distance was called a major arc. What do you call the arc when it's in between? • Question: the video says that ark JK is the shortest distance from J to K, did he mean the shortest distance on the circle? Wouldn't the line segment JK be shorter? • so does the chord need to cross the center?   