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# Geometric constructions: circle-inscribed square

## Video transcript

construct a square inscribed inside the circle in order to do this we just have to remember that a square well we know of squares all four sides are congruent and they intersect at right angles and we also have to remember that the two diagonals of the square are going to be perpendicular bisectors of each other so let's see if we can construct two lines that are perpendicular bisectors of each other and essentially where those two lines intersect our bigger circle those are going to be the vertices of our square so let's throw a straightedge right over here and let's make a diameter so that's a diameter right over here just goes through the circle goes through the center of the circle and two two sides of the circle and now let's think about how it can construct a perpendicular bisector of this and we've done this in other compass construction or construction videos but what we can do is we can put a circle let's throw a circle right over here we got a we got to make its radius bigger than the center what we're going to do is going to reuse this we're going to make another circle it's the exact same size put it there and where they intersect is going to be exactly along those two points of intersection are going to be along a perpendicular bisector so that's one of them let's do another one I want a circle of the exact same dimensions so I'll Center it at the same place I'll drag it out there that looks pretty good I'll move it on to this side the other side of my diameter so that looks pretty good and notice I connect that point to that point I have now I will have constructed a perpendicular bisector of this original segment so let's do that let's connect those two points so that point and that point we could just keep going all the way to so keep going all the way to the end of the circle go all the way over all the way over there that looks pretty good and now we just have to connect these four points to have a square so let's do that so I'll connect to that and that and then I will connect throw another straightedge there I will connect that with that and then two more to go I'll connect this with that and then one more I can connect this with that and there you go I have a shape whose vertices intersect the circle and its diagonals this diagonal and this diagonal these are perpendicular bisectors