IXL - Construct the circumcenter or incenter 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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Learn with an example

question

is the bisector of

∠

and

is the bisector of

∠

Mark the incenter of

△

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

key idea

The incenter of a triangle is the center of its inscribed circle. It is equidistant from all three sides, and it is the intersection of the bisectors of each of the triangle's angles.

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

solution

To construct the incenter of

△

carry out the following step:

Mark the incenter.

Mark the point where
line
A
D
and
line
B
E
intersect. Call it
F
.

Since

is the intersection of two angle bisectors of

△

is the incenter of

△

Looking for more? Try these:

Lesson: Circumscribed circles

Lesson: Inscribed circles

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Teacher tools

Work it out

Not feeling ready yet? These can help:

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

C.7Construct an angle bisector

N.3Identify medians, altitudes, angle bisectors, and perpendicular bisectors

Lesson: Circumscribed circles

Lesson: Inscribed circles

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