IXL - Construct a square inscribed in a circle (Geometry practice)

The diagram below shows a nearly completed construction of a square inscribed in

⨀A

with a vertex at

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

ref_doc_title.

Learn with an example

question

The diagram below shows a nearly completed construction of a square inscribed in

⨀A

with a vertex at

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

key idea

is a diameter of a circle, then the inscribed angle

∠

is a right angle.

To construct the perpendicular bisector of a segment:

At each of the segment's endpoints, draw a circle whose radius is the segment length.

Draw the line through the circles' two points of intersection.

solution

Part of the construction was done for you. Here are the steps to create this part of the construction.

Start with the objects in the diagram below.

Construct the perpendicular bisector of the diameter of

⨀

containing

Draw the line through
A
and
B
.

Mark the point other than
B
where
line
A
B
and
⨀
A
intersect. Call it
C
.

Since

and

are both on

⨀

So,

is the midpoint of

Draw a circle with radius
B
C
centered at
B
.

Draw a circle with radius
B
C
centered at
C
.

Mark the points where
⨀
B
and
⨀
C
intersect. Call them
D
and
E
.

Draw the line through
D
and
E
.

is the perpendicular bisector of

So, it passes through

the midpoint of

Mark the points where
line
D
E
and
⨀
A
intersect. Call them
F
and
G
.

Since

and

are both on

⨀

This means that

is the perpendicular bisector of

Draw the segment between
B
and
F
.

Draw the segment between
F
and
C
.

Draw the segment between
C
and
G
.

start of large bold text, Complete the construction., end of large bold text

To complete the construction of a square inscribed in

⨀A

with a vertex at

carry out the following step:

Draw the segment between
G
and
B
.

Since

is the perpendicular bisector of

and

Since

is the perpendicular bisector of

and

pass through

so they are both diameters of

⨀

Since

and

are diameters, the inscribed angles

∠

and

∠

are all right angles, so

is a rectangle.

is a rectangle with all sides congruent, so it is a square.

Looking for more? Try this:

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Questions
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Time
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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

W.13Angles in inscribed right triangles

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