WEBVTT

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Construct a square
inscribed inside the circle.

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And in order to do
this, we just have

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to remember that a square,
what we know of a square

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is all four sides are
congruent and they

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intersect at right angles.

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And we also have to
remember that the two

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diagonals of the
square are going

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to be perpendicular
bisectors of each other.

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So let's see if we can
construct two lines that

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are perpendicular
bisectors of each other.

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And essentially, where those
two lines intersect our bigger

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circle, those are going to be
the vertices of our square.

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So let's throw a straight
edge right over here.

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And let's make a diameter.

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So that's a diameter
right over here.

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It just goes through
the circle, goes

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through the center
of the circle,

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to two sides of the circle.

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And now, let's
think about how we

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can construct a perpendicular
bisector of this.

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And we've done this in
other compass construction

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or construction videos.

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But what we can do is we
can put a circle-- let's

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throw a circle right over here.

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We've got to make its radius
bigger than the center.

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And what we're going to do
is we're going to reuse this.

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We're going to make
another circle that's

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the exact same size.

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Put it there.

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And where they intersect
is going to be exactly

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along-- those two
points of intersection

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are going to be along a
perpendicular bisector.

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So that's one of them.

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Let's do another one.

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I want a circle of the
exact same dimensions.

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So I'll center it
at the same place.

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I'll drag it out there.

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That looks pretty good.

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I'll move it on to this side,
the other side of my diameter.

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So that looks pretty good.

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And notice, if I connect
that point to that point,

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I will have constructed
a perpendicular bisector

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of this original segment.

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So let's do that.

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Let's connect those two points.

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So that point and that point.

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And then, we could just
keep going all the way

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to the end of the circle.

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Go all the way over there.

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That looks pretty good.

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And now, we just have
to connect these four

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points to have a square.

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So let's do that.

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So I'll connect
to that and that.

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And then I will connect, throw
another straight edge there.

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I will connect that with that.

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And then, two more to go.

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I'll connect this with
that, and then one more.

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I can connect this with
that, and there you go.

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I have a shape whose vertices
intersect the circle.

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And its diagonals, this diagonal
and this diagonal, these

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are perpendicular bisectors.

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