IXL - Construct the inscribed circle and the incenter of a triangle (Geometry practice)

is the bisector of

∠

and

is the bisector of

∠

Mark the incenter of

△

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

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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
C
E
intersect. Call it
F
.

Since

is the intersection of two angle bisectors of

△

is the incenter of

△

Looking for more? Try this:

Lesson: Inscribed circles

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C.7Construct an angle bisector

Lesson: Inscribed circles

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