In my math exam , this question had appeared : http://img33.imageshack.us/img33/6233/44467585.jpg [Broken] (You can click on the link to see the question) I'm having confusion as to what the answer to the question is. I feel that the correct answer to the question would be 2 Direct common tangents , as a common tangent is a tangent is a tangent that is a common tangent to all the circles under consideration.(according to me) However , my teacher feels otherwise and says that there are actually 3 common tangents as there is also a Transverse common tangent to the pair of touching circles in the diagram. Here is a diagram of his view: http://img194.imageshack.us/img194/1092/60396510.jpg [Broken] If we take my teachers view into consideration , then there are 2 transverse common tangents to the first and the last circles too. Hence the total number of tangents goes up to 5. Here is that diagram : http://img20.imageshack.us/img20/9199/20409914.jpg [Broken] However , my teacher does not agree with this. He says that the TCTs cease to be TCTs as they intersect the middle circle. My main question here is with regard to my teachers rather fishy statement "The TCT ceases to be a tangent as it is the secant of yet another circle" . Is he correct? If you think of it in another way and consider separate DCTs for pairs for circles, instead of a single DCT , then the number of tangents can go upto 11. Also , no where in the question is it mentioned that the centers of the circles are collinear. Hence the no of tangents can be 0 also. So what is the correct answer to this ambiguous question?