So you would say that the treasure would have to be right here, which is the center of the circle that passes through the three vertices. As you can see I'm a little bit off but that's just because I was sketching. So there will be one perpendicular bisector, and then here would be another perpendicular bisector and again this is just an estimate to show you how you would solve this problem and then here you'd find your perpendicular bisector and ideally by definition these points are concurrent. So what you would do, if we erased this treasure, is you would draw in your three sides of your triangle and then using your compass you would construct the three perpendicular bisectors of each side. So what you would do to find the treasure is you would have to find the circumcenter of the triangle by drawing those lines. Maybe a tree stump, a grave stone and the beach. Well a common problem that you might see on a test is if they give you three different points and they say, "where's the treasure?" The treasure's located at an equal distance from three random points.
But when will ever apply this in real life? Which means that the center is equidistant from the three vertices. Begin with the line A B 5.Set the compass’s radius to 3, and make a faint circle with the center B.Then, set the compass’s radius to 6, and make a faint circle with the center A.The corner C appears as the intersection between the two circles. And that it passes through all three vertices. Before you construct the circumcircle, you begin by constructing the triangle with the given measurements. So if we take a look at a sketch of what a circumcenter might look like, we notice that it could be a really big circle if you have an obtuse triangle. Which also makes it the center of the circle that's circumscribed about the triangle.
So the circumcenter is where the three perpendicular bisectors of each side intersect. Point of concurrency means you have at least three lines intersecting in one spot. One of the four main types of points of concurrency that we find in triangles is the circumcenter.
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