Geometry Common Tangents To Two Circles
 To enroll in any of our courses, click here

 Common Tangents To Two Circles Theorem: If two circles touch each other (internally or externally) the point of contact lies on the line through the centres.
 People who saw this lesson also found the following lessons useful: Selection of Terms In an A.P. Solving a System of Equations Angles In Alternate Segments Problems on Age Pythagoras Theorem
Example: Find the locus of the centre of a circle of constant radius (r) which touches a given circle of radius r1
(i) externally, (ii) internally, given r1 > r.
Solution: (i) Let O be the centre of the given circle of radius r1, Let O' be the centre of circle of radius r which touches the given circle externally. Then,

OO' = r1+r
O' moves in such a way that its distance from 0{a fixed point) always remains constant equal to r1+ r.
Hence, the locus of C is a circle with centre O and radius r + r1.
(ii) Let O be the centre and r1 be the radius of the given circle. Let O' be centre and r be the radius of the variable circle which touches the given circle internally.
Then,
OO' = r1 - r
O' moves in such a way that OO' remains constant equal to (r1 - r).
Hence, the locus of O' is a circle with centre O and radius r1 - r.

 As many of you know, Winpossible's online courses use a unique teaching method where an instructor explains the concepts in any given area to you in his/her own voice and handwriting, just like you see your teacher explain things to you on a blackboard in your classroom. All our courses include teacher's instruction, practice questions as well as end-of-lesson quizzes for practice. You can enroll in any of our online courses by clicking here. The format of Winpossible's online courses is also very suitable for teachers who are using an interactive whiteboard such as Smartboard on Promethean in their classrooms, because the course lessons can be easily displayed on such interactive whiteboards. Volume pricing is available for schools interested in our online courses. For more information, please contact us at educators@winpossible.com.

 Copyright © Winpossible, 2010 - 2011 Best viewed in 1024x768 & IE 5.0 or later version