geometric construction 3

8/9/2019 Geometric Construction 3

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Geomet r ic const r uct ion 3

Tangent Lines

Tangent Arcs


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TANGENT LINES


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LINE TANGENT TO THE POINTON AN ARC

1. Find the center of the arc, label it point O.

2. Connect points O and C.

3. Extend line OC with the length of theextension equal to line OC. Label the other

end as D.

4. Bisect line OD. Label the intersections as E

and F.

5. Line EF is tangent to arc AB.


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LINE TANGENT TO THE POINT

ON AN ARC Given: Arc AB and point C

A

B

CO

F

E

D


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1. Find the center of an arc. Label the point as

O.

2. Connect points O and C.3. Bisect line OC. Label the midpoint as D.

4. Using D as center and OD as radius, draw an

arc intersecting arc Circle O. Label the

intersection as E.

5. Connect point E to point C. Line EC is tangent

to arc AB.

LINE TANGENT TO AN ARC PASSINGTHROUGH A POINT OUTSIDE THE ARC


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LINE TANGENT TO AN ARC PASSINGTHROUGH A POINT OUTSIDE THE ARC

Given: Arc AB and point C

C+O


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C+

O D


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ARC OF RADIUS R TANGENT TO APOINT ON A LINE

Given: Line AB and radius R

A

B

R

C


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ARC OF RADIUS R TANGENT TO APOINT ON A LINE

1. Draw a line perpendicular to line AB passing

through point C.

2. Using C as center and radius R, draw an arcintersecting the perpendicular line at point

D.

3. Using D as center, draw the circle.


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A

B

CD


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ARC TANGENT TO A POINT ON A LINEPASSINGTHROUGH A POINT OUTSIDE

THE LINE.1. Draw a line perpendicular to line AB passing

through point C.

2. Connect point P and point C.3. Bisect line CP. Label the intersection of line

CB and CP as O.

4. Using O as center and radius equal to OC,

draw a circle.


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ARC TANGENT TO A POINT ON A LINEPASSINGTHROUGH A POINT OUTSIDE

THE LINE. Given: Line AB and radius R

A

B

C

P


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A

B

C

P

O


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ARC EXTERNALLY TANGENT TO

ANOTHER ARC

1. Find the center of the arc. Label the center as O.

2. Connect O to any point along the circumference of

the circle. Label the other point as A. Extend Line

OA.

3. Add to the radius of circle O, the given radius R.

Label the new radius as M.

4. Using O as center and radius M, draw a circle.

Anywhere on the drawn circle is the center of the

circle that is externally tangent to the given arc.


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O

R


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ARC INTERNALLY TANGENT TO

ANOTHER ARC

1. Find the center of the arc. Label the center

as O.

2. Subtract the given radius from the radius ofcircle O, name the new radius as M.

3. Using O as center and radius M, draw a

circle. Anywhere on the drawn circle is the

center of the circle that is internally tangent

to the given arc.


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ARC INTERNALLY TANGENT TO

ANOTHER ARC

Given: Circle O and radius R

R


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O

M


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1. Connect points O and P.

2. Draw line perpendicular to point O and

intersecting the circle at point A. Repeat thestep using point P intersecting the circle at

point B.

3. Connect point A to point B. Label the

intersection of Line AB and Line OP as C.

LINE INTERNALLY TANGENT TOTWO CIRCLES


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4. Using point C as a common point outside of

both circles, and the procedure for

determining point of tangency of a line to a

circle, locate point T1 on circle O and T2 on

circle P.

5. Connect T1 and T2. Line T1T2 is tangent to

circles O and P.



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Given: Circles O and P

O P+

+

A

B

C

T1

T2

T4

T3


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LINE EXTERNALLY TANGENT TOTWO CIRCLES

1. Connect points O and P.

2. Subtract the radius of the smaller circle from

the radius of the bigger and let it be r.

3. Determine the midpoint M of line OP.

4. Using O as center and radius r, draw a circle.

5. Using M as center and radius OM, draw an

arc intersecting circle O at points A and B.6. Draw lines AP and BP.


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7. Draw perpendicular lines from points A, B

and P that intersects circle O at points 1 and

2 and circle P at points 3 and 4.

8. Connect point 1 and 3, and points 2 and 4.

These are the external tangents.


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Given: Circles O and P

O P+ +

rM

a

B

A


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SMOOTH CURVE

1. Using O as center and radius equal to OA,

strike an arc intersecting line OP at point B.

2. Draw perpendicular lines to points A and B.

3. The intersection of the two perpendiculars is

the center of the arc. Label it O.

4. Using point and radius OA a draw the arc.

5. Repeat the steps.


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SMOOTH CURVE

Given: line

AO

T

S

R

Q

P

r

AO

geometric construction 3

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