IXL - Construct the circumscribed circle and the circumcenter of a triangle (Geometry practice)

is the perpendicular bisector of

and

is the perpendicular bisector of

Mark the circumcenter of

△

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Point

Segment

Ray

Line

Circle

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question

is the perpendicular bisector of

and

is the perpendicular bisector of

Mark the circumcenter of

△

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

key idea

The circumcenter of a triangle is the center of its circumscribed circle. It is equidistant from all three vertices, and it is the intersection of the perpendicular bisectors of each of the triangle's sides.

To construct the circumcenter, it is sufficient to find the intersection of two perpendicular bisectors, since the third perpendicular bisector will also pass through this point.

solution

To construct the circumcenter of

△

carry out the following step:

Mark the circumcenter.

Mark the point where
line
D
E
and
line
F
G
intersect. Call it
H
.

Since

is on the perpendicular bisector of

Since

is on the perpendicular bisector of

So,

Since

is equidistant from

and

it is the circumcenter of

△

Looking for more? Try this:

Lesson: Circumscribed circles

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B.15Construct the midpoint or perpendicular bisector of a segment

Lesson: Circumscribed circles

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