## Constructing the Circumcenter

one of the four main types of points of concurrency that we find in triangles is the circumcenter point of concurrency means you have at least three lines intersecting in one spot so the circumcenter is where the three perpendicular bisectors of each side intersect which also makes it the center of a circle that circumscribed about the triangle 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 and that it passes through all three vertices which means that the center is equidistant from the three vertices but when we ever apply this in real life 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 is located at an equal distance from three random points maybe a tree stump a gravestone and the beach so what you would do to find the treasure is you would have to find the circumcenter of the triangle by drawing those lines 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 there would 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 as you can see I'm a little bit off but that's just because I was sketching so you would say that the treasure would have to be right here which is the center of a circle that passes through the three vertices

## How to Construct a 45 45 90 Degree Triangle with a Compass

hi I'm Rachel and today we're going to be going over how to construct a 45-45-90 right triangle with the compass so a 45-45-90 is an isosceles right triangle well if we're making a right angle right a 90 degree angle we can use the compass we can put a point on the piece of paper and just use the ruler to draw a straight line or the part of the compass that's straight to do a straight line there then take the compass so that it forms a perfect 90 degree angle right and you do a point there and then you use your ruler to others or straight edge of some sort to do a straight line like such and that will give you a 90 degree angle then you bring the compass up into the dot and you see where is a 45-degree angle well 45 is half of 90 so it's going to look like just drawing you without a compass something like this right that's half of a perpendicular angle that would be right like this so this is 45 degrees I'll write it out here and this is also ends up being 45 degrees because that forms the perfect triangle and just so you know for the ratio of a 45-45-90 right triangle the sides will be X X and X root 2 in case you're going a little further and doing the sides after you've constructed it with your compass I'm Rachel and thank you for learning with me today