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## Integrated math 2

### Course: Integrated math 2>Unit 11

Lesson 11: Constructing regular polygons inscribed in circles

# Geometric constructions: circle-inscribed equilateral triangle

Sal constructs an equilateral triangle that is inscribed inside a given circle using compass and straightedge. Created by Sal Khan.

## Want to join the conversation?

• Why did Sal go to the trouble of constructing the initial small equilateral triangle before he connected the points where the circle he created intersects with the original circle? That line is (as he shows later) one leg of the larger equilateral triangle he wants to construct.
• he wanted to show why and how it works, not just tell you what to do. This should help you remember it, or at least figure it out yourself if you forget.
• at 203 i think Sal means...'a third of the way around the circle'. but he says triangle. 120 degrees is a third of a circle.
• No, Sal was correct there. A triangle turns 360 degrees from start to finish just like a circle does (or any closed polygon does). That side was 1/3 of the triangle, and just needed to be duplicated 2 more times.
• At . Why does Sal say, " third of the way around the triangle ". What does it mean?
Thanks.
• A triangle's three angles measure up to 180. Since it is a equilateral triangle Sal is constructing,
each angle is 60 degrees. Many people become confused when Sal says 120 degrees is one third of the triangle, but he is talking about the arc of the circle. To find the arc or the angle formed by the arc, use this equation: arcX = 2 angleX. Thus, the angle is 60 degrees and one third of a triangle, due to what I said earlier. (60 x 3 = 180)
• What does it mean to be a secant?
• A line that touches a circle in only two points. So basically a chord that extends infinitely.
• are there easier ways to solve these questions? it takes sal a long time to solve them
(1 vote)
• It's because Sal is explaining them in detail so that people can understand it better.
• Well cant he use this method :
The circumcentre of the triangle we will be going to make will be the center of the circle we are given. So we can make a diameter and treat it like the median of the triangle. Now all the median will intersect at circumcentre and hence the center. Now the intersecting point divides the median in 2:1. So we will be taking 2 as radius and perpendicularly bisect the other one to get 1/2 of radius or 1/2*2=1 and finally the ratio of 2:1.
Now the points of perpendicular bisector intersecting the circle can be connected to the first point of diameter. And its do equal to an equilateral triangle. If you are not understanding this then search for topics circumcircle and medians of equilateral triangle and please answer to this question.
• I get it but how do you do this on paper?
• At , how does Sal get the right place to put the compass?
(1 vote)
• Sal drags the compass so that its center is on the circumference of the original circle and he places it so that it "intersects these two points". The two points are the center of the original circle and the point where one side of the equilateral triangle that is already placed touches the circumference of the original circle.