Tangent Circles and Common Tangents

*Concept of Tangent Circles and Common Tangents

*Tangent Circle

A tangent circle is a line in the plane of the circle that intersects the circle in exactly one point. Tangent circles may be tangent either internally or externally.

Tangent circles are tangent internally if one lies in the interior of the other (except for the point of tangency). Tangent circles are tangent externally if each lies in the exterior of the other (except for the point of tangency). The figure below shows tangent circles with external and internal tangents.

       Externally tangent circles              Internally tangent circles

P

P

*Common Tangent

Common tangents are lines or segments that are tangent to more than one circle at the same time.

fig.1 Two circles may also be tangent to each other.

A common tangent can be tangent either internally or externally. A common internal tangent is a common tangent that intersects the segment that joins the center of the two circles. A common external tangent is a common tangent that does not intersect the segment that joins the centers of the two circles. In the figure below, L1 is the common internal tangent while L2 is a common external tangent.

OO

L2

(2 concentric circles)Concentric circles are circles with the same center.

A

0 external tangents0 internal tangents

(one circle floating inside the other, without touching)

AB0

0 external tangents0 internal tangents

*0 Common Tangents

(2 internally tangent circles)

A B

1external tangent (blue)0 internal tangents

*1 Common Tangent

*2 Common Tangents(2 overlapping circles)

2 external tangents (blue)0 internal tangents

A B

*3 Common Tangents(2 externally tangent circles)

2 external tangents (blue)1 internal tangent (black)

AB

*4 Common Tangents(2 completely separate circles)

2 external tangents (blue)2 internal tangents (black)

AB

*Project In Mathematics

Submitted by:Vincent Yalong&Ellaine Marcelo

Submitted to: Ma’am Rodelyn A. Urbi