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Construct a square[br]inscribed inside the circle.

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And in order to do[br]this, we just have

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to remember that a square,[br]what we know of a square

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is all four sides are[br]congruent and they

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intersect at right angles.

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And we also have to[br]remember that the two

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diagonals of the[br]square are going

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to be perpendicular[br]bisectors of each other.

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

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are perpendicular[br]bisectors of each other.

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And essentially, where those[br]two lines intersect our bigger

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

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

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And let's make a diameter.

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So that's a diameter[br]right over here.

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It just goes through[br]the circle, goes

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through the center[br]of the circle,

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to two sides of the circle.

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And now, let's[br]think about how we

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can construct a perpendicular[br]bisector of this.

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And we've done this in[br]other compass construction

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or construction videos.

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But what we can do is we[br]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[br]bigger than the center.

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

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We're going to make[br]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[br]is going to be exactly

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along-- those two[br]points of intersection

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are going to be along a[br]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[br]exact same dimensions.

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So I'll center it[br]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,[br]the other side of my diameter.

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So that looks pretty good.

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And notice, if I connect[br]that point to that point,

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I will have constructed[br]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[br]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[br]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[br]to that and that.

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And then I will connect, throw[br]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[br]that, and then one more.

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

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I have a shape whose vertices[br]intersect the circle.

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And its diagonals, this diagonal[br]and this diagonal, these

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are perpendicular bisectors.

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