IXL - Construct a tangent line to a circle (Geometry practice)

The diagram below shows a nearly completed construction of a tangent to

⨀A

(the smaller one) through

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 tangent to

⨀A

(the smaller one) through

Complete the construction.

Undo

Redo

Point

Segment

Ray

Line

Circle

Delete

key idea

is the center of a circle and

is a point on that circle, then

is tangent to

⨀

if and only if

is perpendicular to

is a diameter of a circle, then the inscribed angle

∠

is a right angle.

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.

Find the midpoint of

Draw the segment between
A
and
B
.

Draw a circle with radius
A
B
centered at
A
.

Draw a circle with radius
A
B
centered at
B
.

Mark the points where
⨀
A
(with radius
A
B
) and
⨀
B
intersect. Call them
C
and
D
.

Since

and

are both on

⨀

Since

and

are both on

⨀

So,

Similarly,

So,

and

are equidistant from

and

Draw the line through
C
and
D
.

Recall that the set of points equidistant from

and

form the perpendicular bisector of

Since

and

are equidistant from

and

they lie on the perpendicular bisector. So,

is the perpendicular bisector of

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

Since

is the perpendicular bisector of

the intersection

is the midpoint of

Construct a circle that has

as diameter.

Draw a circle with radius
A
E
centered at
E
.

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

To complete the construction of a tangent to

⨀A

(the smaller one) through

carry out the following steps:

Mark a point where
⨀
A
(the smaller one) and
⨀
E
intersect. Call it
F
.

Draw the line through
B
and
F
.

Since

∠

is an inscribed angle in

⨀

and

is a diameter of

⨀

∠

is a right angle.

So,

is perpendicular to

and is a tangent to

⨀

Looking for more? Try these:

Lesson: Tangent to a circle

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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.10Tangent lines

Lesson: Tangent to a circle

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