Ten circular coins are thrown on the street so that no two of them
overlap or touch, and no three of them have a tangent line in common.
What is the total number of lines which are tangent to two of the coins?
Choose the correct option
A) 60 B) 100 C) 180 D) 240 E) 360
There are n(n-1)=2 different ways   of choosing 2 objects from a given collection   of n objects. Thus, there are   10*9/2= 
<gadget id="calculator">  10*9/2</gadget>
<output>45</output>
45   different ways of choosing 2 of the 10 coins.   For each selection of two coins, one can form 4   tangent lines as shown at the right. Therefore,   the answer is   4*45= 
<gadget id="calculator">  4*45</gadget>
<output>180</output>
180.   correct answer 180
<result>C</result>
Ten circular coins are thrown on the street so that no two of them
overlap or touch, and no three of them have a tangent line in common.
What is the total number of lines which are tangent to two of the coins?