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CC Math: HSG.C.A.3, HSG.CO.D.13

Construct a square
inscribed inside the circle. And in order to do
this, we just have to remember that a square,
what we know of a square is 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 straight
edge right over here. And let's make a diameter. So that's a diameter
right over here. It just goes through
the circle, goes through the center
of the circle, to two sides of the circle. And now, let's
think about how we 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've got to make its radius
bigger than the center. And what we're going to do
is we're going to reuse this. We're going to make
another circle that'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, if I connect
that point to that point, 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. And then, we could just
keep going all the way to the end of the circle. Go 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 straight edge 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.