So I’m going to choose side AB and I’m going to swing an arc from point A and I’m going to swing an arc from point B, and this is the trouble with doing these constructions.
We’re going to have to bisect one more side. So I’m going to mark this as perpendicular and I’m going to mark these two segments as being congruent. So those two points are on my perpendicular bisector. Now ideally I would have swung those arcs a little bit further apart but I can pick up where my two points are. So I’m going to swing an arc from point A making sure that my compass doesn’t move too much, I’m going to swing an arc from point C and I see that I have my perpendicular bisector. So the first thing I’m going to do is I’m going to grab my compass and I’m going to bisect this side AC. So if I want to find the point of concurrency of the three perpendicular bisectors we will have our circumcenter. So I’m going to grab my straightedge and I’m going to connect A and C, I’m going to connect B and C and I’m going to connect A and B. So first thing I’m going to do is I’m going to draw in the three sides of this triangle. So it sounds like if we found the circumcenter that will be the answer to our problem. If I found that point of concurrency then it would be the center of this circumscribe circle, which would be equidistant from the three vertices. So here I have points AB and C and I want to find the point that is equidistant from these three, but what are we going to do? Well we can start by asking ourselves if we found the circumcenter will that help? Well to find the circumcenter we’d have to do the three perpendicular bisectors, in order to do that we need a triangle. In this problem it says find the point that is equidistant which means the same distance from AB and C.
Let s take a look at an application of what we know about points of concurrency.
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