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## Constructing circumcircles and incircles

Current time:0:00Total duration:2:22

# Geometric constructions: triangle-circumscribing circle

CCSS.Math:

## Video transcript

Construct a circle
circumscribing the triangle. So that would be a circle that
touches the vertices, the three vertices of this triangle. So we can construct it using
a compass and a straight edge, or a virtual compass and
a virtual straight edge. So what we want to do is center
the circle at the perpendicular bisectors of the sides,
or sometimes that's called the circumcenter
of this triangle. So let's do that. And so let's think
about-- let's try to construct where
the perpendicular bisectors of the sides are. So let me put a
circle right over here whose radius is longer than
this side right over here. Now let me get one
that has the same size. So let me make it the same
size as the one I just did. And let me put it
right over here. And this allows us to construct
a perpendicular bisector. If I go through that point and
this point right over here, this bisects this
side over here, and it's at a right angle. So now let's do that
for the other sides. So if I move this over
here-- and I really just have to do it for one
of the other sides, because the intersection
of two lines is going to give me a point. So I can do it for this
side right over here. Let me scroll down so you
can see a little bit clearer. So let me add another
straight edge right over here. So I'm going to go
through that point, and I'm going to go
through this point. So that's the
perpendicular bisector of this side right over here. And I could do the
third side and it should intersect at that point. I'm not ultra, ultra precise,
but I'm close enough. And now I just have to
center one of these circles. Let me move one of these away. So let me just get
rid of this one. And I just have to move this
circle to the circumcenter and adjust its radius so that
it gets pretty close to touching the three sides, the three
vertices of this triangle. It doesn't have to be perfect. I think this exercise has
some margin for error. But they really want
to see that you've made an attempt at
drawing the perpendicular bisectors of the sides,
to find the circumcenter, and then you put a
circle right over there.