Tangent Circles Group 6 Charity

7/27/2019 Tangent Circles Group 6 Charity

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TANGENT

CIRCLESGROUP 6III - CHARITY



REVIEW :

A is a line

that intersects thecircle at exactly one

point called the

tangent

point of tangency



A line segment or a

ray can be tangent

to a circle if it is apart of the line that

is tangent to the

circle



The radius of a

circle is

perpendicular to

the point of

tangency



TANGENT CIRCLES



Common tangents are

lines or segments thatare tangent to more than

one circle at the sametime. It is a line that is

tangent to each of two

coplanar circles



A common tangent can be tangent

either internally or externally.

A common internal tangent is acommon tangent that intersects the

segment that joins the center of the

two circles.

A common external tangent is a

common tangent that does notintersect the segment that joins the

centers of the two circles.



Line L2 is a common external tangent

while line L1 is a common internal



4 Common Tangents (2 completely separate circles)

2 external tangents (blue)

2 internal tangents (black)



3 Common Tangents

(2 externally tangent circles)


1 internal tangent (black)



2 Common Tangents

(2 overlapping circles)


0 internal tangents



1 Common Tangent(2 internally tangent circles)

1 external tangent (blue)

0 internal tangents



(2 concentric

circles)

Concentric circles

are circles

with the samecenter.

0 external tangents

0 internal tangents

(one circle floating

inside the other,

without touching)

0 external tangents

0 internal tangents



The common tangent that connects thecircles will be replaced by a common

secant because it intersects a circle in

more than one point.



Tangent circles may be tangent

either internally or externally.

Tangent circles are tangentinternally if one lies in the interior

of the other (except for the point of tangency).

Tangent circles are tangentexternally if each lies in the

exterior of the other (except for the

oint of tan enc .



The circles areexternally tangent. The circles areinternally tangent.



HOW TO SOLVE FOR THELENGTH OF THE COMMON

TANGENT OF THE TWOCIRCLES



Draw the segment connecting the

centers of the two circles and draw the

two radii to the points of tangency



From the center of the smaller circle, draw a segment

parallel to the common tangent till it hits the radius of thelarger circle.

You end up with a right triangle and a rectangle; one of

the rectangle’s sides is the common tangent.



You now have a right triangle and a rectangle and

can finish the problem with the Pythagorean

Theorem and the simple fact that opposite sides of

a rectangle are congruent.



GROUP 6

III - CHARITY PONCE, JOYCELEIGH

URGENA, ROIE

ENRIQUE, MARNALYN

AQUINO, KRYSTYNA

THANK YOU!!!

Tangent Circles Group 6 Charity

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