



 
Manish, Your are right  there are an infinite number of tangents to a circle, and each of these has a second, parallel tangent (on the 'opposite side' of the circle). The book seems to be answering a different question: In math (and some other areas like computer science) a source of confusion can be: which terms are 'Universal Quantifiers' (For All ... ) and which are 'Existential Quantifiers' (There Exists .... ) Here the question seems to unpack as: You are answering the question: Both questions have answers (and different answers!) so it is a matter of figuring out which question to answer! Walter Whiteley
 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 